The sheltering of Nazi war criminals in South and Central America is something most of us know a little bit about. In the decades following the second World War, various commandants, martial hoodlums and Holocaust strategists were tracked down in the most settled of circumstances.

Cinema has not had much to say about the gaps between flight and arrest (or death). Lucía Puenzo's fascinating, original Wakolda (The German Doctor) seeks – among other things – to rectify that situation. Adapting her own novel, the Argentinean film-maker has built a coming-of-age drama around the later adventures of Dr Josef Mengele. Florencia Bado plays a young girl who encounters the doctor, notorious for his experiments on patients in Auschwitz, while living with her parents at a hotel in Patagonia. This is 1960, a full 19 years before Mengele apparently drowned in a swimming accident while at large in Brazil.

“We know quite a bit about his movements,” Puenzo says. “He was in Buenos Aires for four years. He actually appeared in the phone book as ‘Jose Mengele’. He had absolute immunity before the trials began. Until then people didn’t know much about the doctors. He lived a normal life. The information popped out. He vanished for a while, but we know that he did turn up in Patagonia for a while.”

Puenzo, the daughter of the great film director Luis Puenzo, goes on to explain the complex history of Argentinean attitudes to the ghastly men the nation once sheltered. There was, she argues, immediate revulsion among the public when the information became generally known. But the issue is dragged up in political debate to this day. Juan Perón, in power from 1946 to 1955, remains a hard figure to pigeonhole. Indeed, he still garners some support from the left.

“It was not military rule,” she says. “In other parts of South America there was military rule. But Perón did many other good things. But not even the most passionate Perónista is able to defend what he did as regards war criminals. This is still a discussion because the right-wing will point out that, though Perón may have done good things, he allowed this to happen. Of course, much of it was about money. There was all this Nazi gold coming in.”

Born in 1976, Puenzo is just about old enough to remember friends worrying about peculiar old men living in unexplained comfort. The issue was discussed.Indeed, it was a cause of great anguish for many Argentineans.

“Oh, it was an eternal shame. And, when it eventually came out, nobody much tried to say it’s okay. I remember speaking with my grandmother, who was a history teacher in the 1960s. As soon as it became well known, it was something people were very uncomfortable with.”

An endlessly chatty, intensely articulate woman with a great deal of agitated hair, Puenzo was born and raised in Buenos Aires. Her impeccable English can be attributed to that fact that she attended a “Scottish school” in the Argentinean capital. We forget that the modern nation is very much the creation of immigrants: Italian, Spanish, Irish, Scottish. She further honed her English when visiting Dublin during the mid-1990s.

“Yes I spent six months there when I was 19,” she says. “I was backpacking across Europe and I liked it so much I stayed. I worked in a bar and lived in a hostel. That was such a great time.”

Luis, her father, is best known for the 1985 film The Official Story. Addressing the "disappearances" of the late early 1980s, the film won the Oscar for best foreign language film and brought Luis to Hollywood for a spell. In 1989, he directed Gregory Peck and Jane Fonda in Old Gringo. Puenzo remembers her father gently prodding her towards her current career.

"I was eight years old when he won his Oscar," she remembers. "That was exciting. His films were part of our lives. The Official Story was shot in our house. The girl's room in the film was my room and I remember taking a sleeping bag to the kitchen. What I remember most was the fun that he brought to film sets. And I've tried to carry that on."

Lucía went on to study literature at the University of Buenos Aires before making her way to the National Film Institute. Even now, she alternates film scripts with novels and short-story collections. Her debut feature XXY, the story of a teenage intersex person, won the grand prize at Cannes Critics' Week and took the Goya Award for Best Spanish Language Foreign Film in 2007.

Wakolda is the sort of project that could edge her into the mainstream (if that is where she wants to go). The child's story is easy to identify with. Her interactions with Mengele – who seeks to trigger a growth spurt through dubious "experimental" procedures – are creepy and intriguing. And, of course, we remain fascinated with the Nazis. Puenzo is careful not to present Mengele – played with restraint by Àlex Brendemühl – as any sort of cackling monster. Sinister waves hang around him, but he remains a fleshy human being.

“It was important not to fall into the stereotype of the monster,” she says. “These characters were much more complex. We have so many testimonies of how they could disguise their personalities and become perfect citizens. So many people came out to say when they were discovered: ‘Oh but he seemed like such a nice old man.’ For me that was the most scary part; they could be demons and then be perfect citizens for the rest of their lives.”

Puenzo is eager to clarify that the young girl’s story remains at the heart of the film. We are lured in by the promise of a legendarily ghastly villain and then charmed by this more delicate story of growing up as an awkward child.

“Yes, that’s right. It’s more about her than it’s about Mengele,” she says. “It’s about the spirit of life that you have when you’re becoming an adult. It’s about learning who your parents really are.”

Lucía Puenzo is steeped in film. Her three brothers are all involved in the business. Her husband is a writer and a film director. Her father, of course, is a senior figure in the business. Yet she is eager to maintain an identity as a novelist. When her next collection of short stories is finished, she will, however, throw herself into film projects set in Brazil, Mexico and Paris. “I keep busy. I keep busy,” she says.

And with a flourish she is gone. This whirlwind will come our way again soon.