Preheat the oven to 450°F (230°C). Position a rack in the middle of the oven and lightly grease a baking sheet.

Heat a large, high-sided skillet over medium-high heat. Add the 1/4 cup olive oil. Add the broccoli rabe, season with salt and pepper, and sauté until wilted, about 3–4 minutes.

Add the 1/2 teaspoon crushed red pepper flakes and the 2 cloves minced garlic to the skillet and cook another 30 seconds to 1 minute, until fragrant. Remove the skillet from the heat and leave the oil in the pan; transfer the cooked broccoli rabe to a bowl or plate.

Lightly flour your work surface. If making two pizzas, divide the 1 pound of dough in half; otherwise use the full amount for one pizza. Use your hands or a rolling pin to flatten and stretch the dough into your desired shape and thickness. Place the shaped dough onto the greased baking sheet.

Use a spoon to drizzle some of the olive oil left in the skillet over the dough to lightly coat the surface (this will act as your "sauce"). Spread the 1/3 cup halved kalamata olives over the dough, then distribute the cooked broccoli rabe evenly. Sprinkle half of the 1/2 cup finely chopped basil over the toppings.

Tear or slice the 8 ounces fresh mozzarella and scatter most of it over the pizza (reserve a little if you prefer). Add the 8–10 slices pepperoni, if using. Season lightly with salt and pepper.

Bake the pizza in the preheated oven for 8–10 minutes, or until the mozzarella is melted and the crust is golden.

Remove the pizza from the oven. Tear the 8 ounces fresh burrata into pieces and distribute it over the hot pizza. Return the pizza to the oven just until the burrata is warmed and slightly softened, about 1–2 minutes.

Remove the pizza, sprinkle with the remaining basil, and season with additional salt and pepper to taste. Let rest briefly, slice, and serve immediately.