Mix warm water, yeast, and a pinch of sugar in a bowl, then let sit until frothy, about 5 minutes—this activates the yeast.
Add flour, salt, and olive oil to the yeast mixture. Stir with a spoon until the dough begins to come together.
Turn the dough onto a floured surface and knead for about 8–10 minutes until smooth and elastic. Cover with a damp cloth and let rise in a warm spot for 1 hour, or until doubled in size.
Preheat your oven to 475°F (245°C). Punch down the risen dough and roll it out into a 12-inch circle on a floured surface.
Transfer the dough to a pizza peel or baking sheet. Spread a generous layer of pizza sauce evenly over the surface, leaving a small border around the edges.
Arrange slices of spicy pepperoni evenly over the sauce, pressing them down gently to ensure they stay in place.
Bake the pizza in the preheated oven for 12–15 minutes, or until the crust is golden and bubbling around the edges, and the pepperoni edges are crispy.
Carefully remove the pizza from the oven and transfer it to a serving surface. Tear the burrata into chunks and evenly distribute over the hot pizza while it’s still warm, allowing it to melt slightly.
Finish with a drizzle of olive oil or a sprinkle of fresh basil if desired. Slice into wedges and serve immediately for the best combination of textures and flavors.