Preheat oven to 375 degrees F.
To make the pesto, combine the basil, garlic, pine nuts, cheese, lemon, salt and pepper. Pulse a few times to chop everything down. While the machine is running, slowly stream in enough olive oil to create a sauce. Taste and adjust seasoning accordingly, adding more salt or pepper as needed. Set aside.
Cut the pizza dough in half and roll out each half on a lightly floured work surface to about 1/2-inch thick rectangles. Place on a oiled baking sheet. Brush the tops of each with olive oil and season with Italian seasoning. Bake until golden brown and crispy, about 18 to 20 minutes.
Toss together the cherry tomatoes, olive oil, salt and pepper on a baking sheet. Roast in the oven for about 15 minutes, until soft and slightly charred. Remove from the oven and let cool.
Spread a little pesto on the bottom of an oven-safe baking dish. Sprinkle with a third of mozzarella cheese on top. Top with half of the cherry tomatoes. Then repeat with some more pesto, more mozzarella, and more cherry tomatoes. Bake until the cheese is bubbly and melted, about 15 to 20 minutes. Remove from the oven and serve immediately with the flatbread.