MAKES ONE 12-INCH PIZZA; SERVES 2–4
Place a pizza stone on a rack in the lower third of the oven and preheat to 450°F. Let the pizza stone heat for 45–60 minutes.
In a bowl, combine the eggplant, onion,¼ cup olive oil, and the salt. Spread in an even layer on a rimmed baking sheet and place the baking sheet on top of the hot pizza stone in the oven. Roast, turning vegetables over about every 10 minutes, until the eggplant is tender and lightly golden, about 35 minutes.
Place a large sheet of parchment paper on a pizza peel or large rimless baking sheet and place the ball of dough in the center. Coat your fingers with oil and press the dough from the center outward into a 12-inch round with a slightly raised edge. If the dough springs back, cover it with a kitchen towel and let it rest for a few minutes, then continue. Patience is the key here, as the thinner the dough is, the crisper the crust will be. Cover the dough round with a kitchen towel and let rise for 15 minutes.
Brush the raised edge of the dough with a light coating of olive oil. Arrange the peppers on the dough, leaving a ½-inch border uncovered. Arrange the eggplant and onion on top of the peppers, and then sprinkle with the oregano and season to taste with pepper. Top with the cheese and capers. Carefully slide the pizza-topped parchment paper from the peel or baking sheet onto the hot pizza stone. Bake until the crust is golden brown and the cheese is bubbling, 9–12 minutes.
Using the pizza peel or rimless baking sheet, remove the pizza from the oven and transfer it to a cutting board. Let the pizza stand for 1 minute, and then slice and serve.