Place a pizza stone in the oven if you are using one. If you aren’t, line a baking sheet with parchment paper that is dusted with a bit of flour and cornmeal. Preheat the oven to 550°.
In a large pan, pour 2 tablespoons of oil into a large skillet, add onions, place over low heat, and cook until the onions just start to caramelize, 6–7 minutes.
In a small bowl, toss 1 tablespoon olive oil with mushrooms.
Sprinkle flour over a clean countertop and begin to prepare your pizza dough. Press down into the center of the ball of dough with your fingertips to form a circle. Keep pressing the dough outward until it is 16 inches in diameter, about 1/4 inch thick in the center, and 1 inch thick at the crust. If using a pizza peel and pizza stone, sprinkle the peel with a bit of flour and cornmeal and gently place the dough on top of it. If you’re using a sheet pan lined with parchment, place the dough in the pan.
With a spoon, spread pizza sauce evenly around the dough. Place mozzarella slices over the sauce so they are evenly spaced and not overlapping. Sprinkle onions, sausage rounds, and mushrooms over the cheese.
Slide the pizza into the oven (either directly onto the hot pizza stone if using a peel or onto the rack if using a baking pan) and bake until the crust is golden brown and the cheese is bubbling with light brown spots, about 12 minutes.
Drizzle pizza with olive oil (especially on the crust). Sprinkle with sea salt and chopped basil. Slice and serve warm.