Position a rack in the middle of the oven and preheat to 425°F.
Heat the oil in a heavy medium skillet over medium-high heat. Add the bell pepper and sprinkle with salt and pepper. Sauté until beginning to brown, about 5 minutes. Add the chopped onion and sauté until starting to brown, about 4 minutes. Stir in the crushed red pepper and remove from the heat.
Unwrap the pizza. Sprinkle the Parmesan cheese over. Place directly on the middle oven rack (no pan) and cook until the crust edges are deep brown, 11-13 minutes. Transfer the pizza to a work surface and let stand 3 minutes. Spoon the pepper-onion mixture over. Top with arugula or radicchio, if desired. Cut into 6 wedges and were right away.