Preheat a largebaking sheet in a 475°F oven.
Brush the top of thenaan with 1/2 tablespoon of the olive oil.
In a medium bowlusing a fork or back of a spoon, gently smash and stir the cherries withbalsamic vinegar, 1/4 teaspoon of the salt, the pepper, and remaining 1tablespoon olive oil. Thinly slice 6 of the basil leaves and stir into cherrymixture. Spread the cherry mixture onto both naan.
Transfer the naanflatbreads onto the hot baking sheet and bake until crisp, about 7 minutes. Topwith the burrata and bake until the burrata is fully heated through, about 3minutes more.
Sprinkle with the remaining1/8 teaspoon salt, 6 basil leaves and, if desired, hot pepper flakes. Sliceinto 3 pieces each to serve.
