In researching past shows, she'd been all over America, looking for the ways that Italian food had influenced American cooking, and vice versa, only to realize that "Italians are not the only ones who have this kind of food phenomenon," she said.
"The mix of America is all these different ethnicities and I think that the strength of the fiber of America is just that," she said.
"I was an immigrant. I came here at 12," said Bastianich, whose family came from Pula, a city that was once part of Italy, was later part of Yugoslavia and is now in Croatia. "We were caught behind the Iron Curtain until I was 10," she said, and spent two years in a political refugee camp in Italy before coming to the U.S.
When she turned 18, she became a citizen right away because, "I wanted to belong someplace. I wanted to have a country," she said.
For the show, "I thought, well, you know, America, the Fourth of July, immigrants, we all celebrate this great country on the Fourth of July, let me capture . . . how great this country really is and allow the celebration of all these other ethnicities within this greater whole."
She wasn't initially familiar with the celebration of Juneteenth, but "I loved it," she said of the holiday that marks June 19, 1865, when news of the abolition of slavery was announced in Texas, more than two years after the Emancipation Proclamation was to have taken effect.
"When they found out, they celebrated. And they still celebrate it to this day. [So do people in at least 42 states, and in Philadelphia.] And I found it wonderful," said Bastianich, who was accompanied in Galveston by actress Anna Deavere Smith.
Bastianich describes herself as competitive - check out her lawn-bowling technique at Pepin's Bastille Day party - but she's not a fan of most of the current cooking-competition shows.
"I think it's all about sensationalism," she said of most she's seen. "And I think, you know, people just like to be stimulated and kept on tension with who's going to win. But it has nothing to do with food. It has nothing to do with what food really is. It's a nurturing element, it's communicating, it is alive."
Bastianich did confess to a fondness for the Food Network's "Chopped," with its mystery baskets of ingredients.
"When I see those young chefs . . . get their baskets, I try to think, 'What would I do with the basket?' "