Heat grill. Set pizza stone on grill rack and allow to get very hot. If you do not have a pizza stone, preheat oven to 500°F and prepare pizza as directed below, except bake it on a nonstick sheet pan until crust browns on edge, about 10 to 12 minutes.
Sprinkle cornmeal on an upside-down cookie sheet or a pizza peel. Lay pizza crust on cornmeal.
Place garlic, arugula, basil, olive oil, Parmesan, salt and pepper in a food processor and process to form a paste; spread over pizza dough. Dot with goat cheese.
Slide pizza onto preheated stone, cover and let cook until crust is crisp and puffed, about 10 minutes. Remove to cutting board and cut into four slices. Yields 1 slice per serving.