When CBS News' Alex Wagner was 12 years old, she had a "revelation" at a diner.

"My dad had gone to the restroom, and I was asked by the line cook, 'Are you adopted?' And it was the first time I thought, 'Oh, wait a second, maybe everyone else doesn't see me as generically American as I understand myself to be," Wagner said Tuesday on "CBS This Morning."

The only child of a Burmese mother and American father, whose roots trace back to Ireland and Luxembourg, the CBS News correspondent said she grew to become "this kind of exotic, hapa, 'futureface.'"

"It was exciting and interesting and fun. But at a certain point, especially as I got older, I wanted – that felt too rootless. I wanted meaning," Wagner said. "I wanted to find a sense of belonging and identity."

Raised in a predominately white community, she said she identified more with "white culture," but she started to question: "Where is the Burmese side of my history? Where is that made manifest?"

So she set out on a quest, she said, to dig into her family history. She chronicles her search from Burma to Luxembourg for answers in her new book, "Futureface: A Family Mystery, An Epic Quest, and the Secret to Belonging."

"I think all Americans, especially right now, want to find themselves in the American story. We're so fractured as a country. There is such a question about identity, who belongs here, what is the immigrant story, and how does it dovetail with the American story. That's a fundamental question right now, right? And I wanted to find out what kind of American am I, which means who were my American forefathers?" Wagner said.

She said she found that "a lot is lost when you immigrate to America."

"That is partly by necessity but also because we like to exfoliate the bad parts of our story. And what I did was go back to the homelands and find the ugly parts of the story and write about them because I think part of becoming whole is accounting for all the sins and all the warts and all the fissures that are part of everybody's story."

She said as immigrants, people leave things that are broken in their own countries.

"We didn't just arrive here on American shores virtuous, perfect immigrants, virtuous new citizens of a country. We had our own baggage. And part of this moment I think is reconciling that American baggage," she said.

And in America, a "salad bowl" nation where different individuals and ingredients come together, "the question is, how does that all coalesce?"

"We're all so different. We all taste and look and smell and sound and believe different things. How do we make a democracy out of that?" Wagner said.