How to Make It
Adjust an oven rack to the middle position and preheat the oven to 400°F. Put the pizza dough on a lightly oiled cutting board and cover with a damp kitchen towel. Coat a rimmed sheet pan with 1 tablespoon oil and set aside.
Toss the eggplant with 2 tablespoons oil, the paprika, fennel, oregano, 1 teaspoon salt, and pepper in a large bowl. Turn the eggplant out onto the prepared sheet pan and roast until just tender, about 10 minutes. Transfer the eggplant to a heatproof bowl and set aside.
Increase the oven temperature to 475°F. Coat the pizza dough with about 1 tablespoon oil and place it on your work surface. Roll the dough into a rustic oval shape, about – to 1/4-inch thick, then place it in the sheet pan. (If your dough is soft enough, you can also simply stretch it out in the pan.) Cover with a damp kitchen towel and let it rest for 10 minutes.
Toss the onion rings with 1 teaspoon oil and the remaining 1/2 teaspoon salt in a medium bowl. Sprinkle the eggplant over the dough (scattering the vegetables all the way to the edge) and place the onion rings over the eggplant. Evenly sprinkle the provolone over the onions and drizzle with the remaining 2 teaspoons oil. Sprinkle with the crushed red pepper flakes.
Bake until the provolone melts and the crust is cooked through and golden, 12 to 15 minutes.
Preheat the broiler to high, sprinkle the Parmigiano-Reggiano over the pizza, and return it to the oven. Broil until the top of the pizza begins to blister in spots, 2 to 3 minutes (watch it closely, since broiler intensities vary).
Remove the pizza from the oven and, with a spatula to help, pop it out of the pan, and slide it onto a cutting board. Sprinkle with the basil leaves, slice into pieces, and serve.