Preheat an oven to 450 degrees F. Line two baking sheets with parchment paper and set aside.
Lightly dust a work surface with all-purpose flour. Carefully stretch both balls of pizza dough out into a rectangle about 12 inches long and 8 inches wide (the dough should be between 1/4- and 1/2-inch thick). Scatter the mozzarella, tomatoes, basil and pepper flakes evenly over each piece of dough. Drizzle the olive oil evenly over both portions of dough and season them with salt and pepper.
Starting on the wider side of the dough, roll each piece of dough into a log. Slice each log into 6 equal portions and transfer the rolls to the prepared baking sheets, leaving at least 1 inch between each roll.
Bake the pizza rolls, rotating the pans halfway through baking, until deep golden brown, about 25 minutes. Let the rolls cool slightly before serving them warm (if packing them up for a picnic, let them cool completely).
NotesCook's Notes: The fresh mozzarella has to be very dry for these rolls to keep their shape. If your fresh mozzarella is packed in water, lay the slices out on a few sheets of paper towel and let them dry out for a couple of minutes. You can also use shredded mozzarella to guarantee a successful turnout.
COOK'S PERKS! As some of the mozzarella melts during baking and caramelizes on the parchment paper, it makes a delicious snack - to the victor go the spoils!