Cut the base of the stems off the chanterelles. Wipe any gritty mushrooms clean with a damp paper towel. Tear any large mushrooms into bite-sized pieces, and leave any smaller ones whole.
Warm unsalted butter in a large skillet over medium-high heat. Add the chanterelles and cook, stirring occasionally, until tender (about 5 minutes). During the last minute, stir in minced garlic. Season mushrooms to taste with kosher salt and pepper, then set aside.
Preheat an oven to 500°F, and set an oven rack in the lowest possible position. Lightly coat a pizza pan with nonstick cooking spray.
Stretch pizza dough into a round large enough to fit the pizza pan. Very lightly drizzle the dough with olive oil, using your hands to evenly spread the oil around. Sprinkle dough with a small pinch of kosher salt. Top pizza evenly with grated mozzarella cheese, crumbled goat cheese, sautéed chanterelles and rosemary. Finish with a sprinkling of kosher salt and black pepper, then an even dusting of Parmesan cheese.
Transfer pizza to the oven on the lowest rack and cook until the crust is golden brown (bottom and crust) and the cheese is nice and bubbly (9 - 11 minutes). Drizzle pizza very lightly with truffle oil before serving.