An hour before cooking, place a pizza stone in oven and preheat to 500°F.
While the oven preheats, combine tomatoes, garlic, olive oil, and a pinch of salt in a small bowl. Stir with a spoon and let marinate for 15–60 minutes.
Dust a clean countertop with flour to prevent the dough from sticking. To stretch the dough, start by pressing down in the center of the ball, using your fingers to flatten the center. Gently push the dough out from the center to form the crust, leaving a 1 1⁄2-inch rim around the circumference of the pizza. Stop when the pizza is approximately 12 inches in diameter. Transfer it from the countertop to a pizza peel.
Drape the sliced zucchini over the dough. To keep the zucchini from making the crust soggy, twist and curl slices so they don’t lie perfectly flat. Layer the blossoms over the zucchini slices. Add half the marinated tomatoes, allowing liquid to drain back into bowl.
Transfer the pizza from the peel to the pizza stone. Bake at 500°F for 6 minutes.
Remove the pizza from the oven. Use your hands to pull the fior di latte or mozzarella into pieces approximately 2 inches in diameter. Disperse evenly across the pizza and then scatter the grated Parmigiano Reggiano over the surface.
Return pizza to oven and bake an additional 3–4 minutes to allow the cheese to melt.
Remove the pizza from the oven. Finish it with the remaining tomatoes. Scoop the burrata onto the center of the pizza, allowing it to ooze slightly out. Scatter basil leaves across the top of the pizza. Finish with salt and freshly ground pepper to taste and a drizzle of extra-virgin olive oil.