In a small bowl, stir together the yeast, sugar, and warm water. Let stand until foamy, about 5 minutes.

Add the flour to the bowl of a stand mixer fitted with the dough hook. Sprinkle the salt over the flour and mix on low speed for 15 seconds to distribute salt.

Add the olive oil, room-temperature water, and yeast mixture and mix on low speed for 1 to 2 minutes, then increase the speed to medium and mix until a ball of dough forms, about 5 minutes.

Spray a medium bowl lightly with cooking spray. Shape the dough into a ball and set it in the bowl seam side down. Cover the bowl with plastic wrap and place in a warm area until doubled in size, about 60 minutes.

When the dough is almost risen, place a cast-iron pizza stone on the center rack of the oven and preheat the oven to 500F.

When the dough has risen, remove the plastic wrap and push down on the dough to release the gases and bubbles. Shape it into a ball. Stretch the dough into a 14-inch round on a sheet of parchment. Drizzle with the olive oil and top evenly with the mozzarella and tomatoes. Sprinkle evenly with the salt and pepper.

Transfer the pizza and parchment to the hot pizza stone. Bake until the crust is golden and the cheese is beginning to brown in spots, 13 to 15 minutes.

Transfer the pizza to a cutting board, top with the basil, cut into 8 slices, and serve.