Thirty to sixty minutes before baking the pizza, place a baking stone on a rack in the lowest level of the oven; preheat oven to 500°.
Place the dough on a floured surface; holding your hands flat, pat the ball out evenly with your fingers, lifting it and turning it over several times, until it reaches a 9-inch circle—do not handle the dough any more than is necessary; if the dough seems sticky, dust it lightly with flour.
Dust a pizza peel or a rimless cookie sheet with flour.
Carefully transfer the circle of dough to the peel; shake the peel once or twice to make sure the dough does not stick; if it does, sprinkle the peel with more flour.
Quickly scatter the goat cheese and Gorgonzola; distribute both mozzarella and smoked mozzarella slices over all; drizzle with the oil.
To slide the pizza onto the baking stone, line up the edge of the peel with the back edge of the stone, then tilt the peel, jerking it gently to start the pizza moving.
When the edge of the pizza touches the stone, carefully pull back on the peel until the pizza is completely off.
Once the pizza is on the stone, do not attempt to move it until it firms up in 2-3 minutes.
Bake 6-7 minutes, or until the dough is crisp and browned; serve immediately.