Expect the crust to char a bit; it adds to the flavor.
Set peppers over grates on gas burners set on medium flame. Cook, turning often with tongs, until pepper skins are black and blistered, about 10 minutes. Remove from heat, and transfer to a metal bowl; cover with plastic to steam, about 15 minutes. Remove from bowl; rub blackened skin away. Core and seed peppers; cut them into 1/4-inch-wide strips. Set aside.
Build a medium-hot fire in outdoor grill, or set grill pan on stove over medium-high heat. Divide pizza dough in half. Working on a clean baking sheet greased with 1/2 tablespoon olive oil, use your fingers to flatten and stretch half the dough into a rough 10-inch circle or rectangle. Let rest a few minutes; then carefully stretch again, as dough will shrink. The dough should be as thin as possible without tearing.
Transfer dough to grill, and cook until bottom side is golden brown and top side starts to bubble, 3 to 5 minutes. Quickly turn crust over, and cook about 2 minutes more to ensure that crust cooks through. Turn crust over again. Scatter half the peppers and half the prosciutto over crust; sprinkle with half the Parmesan cheese. Cover grill, and let cook until toppings are hot and bubbly, 6 to 8 minutes. Remove from grill, and slide pizza onto a cutting board. Drizzle with olive oil, and season with salt and pepper. Repeat process with remaining dough and toppings. Cut into wedges, and serve.