Place a pizza stone or inverted baking sheet on the center rack and preheat oven to 500°F. Let the dough rest at room temperature for 30 minutes if refrigerated. On a lightly floured surface, stretch or roll the dough into a 12-inch round, working from the center outward and leaving a slightly thicker edge for the crust.

Transfer the dough to a piece of parchment paper. Brush the surface lightly with olive oil, then use your fingertips to press dimples across the center. This prevents large bubbles and helps the pesto adhere.

Spread the pesto evenly over the dough, leaving a 3/4-inch border. Arrange mozzarella slices across the surface, then scatter cherry tomatoes cut-side up. Sprinkle with Parmesan and red pepper flakes if using.

Slide the pizza, parchment and all, onto the preheated stone. Bake until the crust is deeply golden and blistered in spots and the cheese is bubbling with light brown patches, 10 to 12 minutes. Rotate halfway through if your oven has hot spots.

Remove from oven and let rest 2 minutes. The tomatoes will have softened and released some juices - this is perfect. Scatter fresh basil over the top, slice, and serve immediately.