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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.
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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.
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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.
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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.
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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.