Any strong-flavored cheese, such as Gruyere, can be substituted for the Fontina.
Fill a medium saucepan with cold water. Add potatoes; salt well. Bring to a boil over high heat. Reduce heat, and let simmer until potatoes are fork-tender, about 20 minutes. Remove from heat, and drain. When cool, cut into 1/4-inch-thick rounds, and set aside.
Meanwhile, heat 2 tablespoons olive oil in a large skillet over medium heat. Add onions and thyme, and cook, stirring, until onions are very soft and translucent, about 15 minutes. Remove from heat, and set aside.
Build a medium-hot fire in outdoor grill, or set grill pan on stove over medium-high heat. Divide prepared pizza dough in half. Working on a clean baking sheet greased with 1/2 tablespoon olive oil, use your fingertips 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 think 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. Spread half the onion mixture over crust. Scatter with half the potatoes and half the Fontina and Parmesan cheeses. Cover grill, 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.