Pre-heat oven to 550 F° (or as hot as your oven will go).
Place a pizza stone on the middle rack and let the stone heat for at least 20 to 30 minutes.
In a large skillet, heat the olive oil over medium-high heat.
Add the mushrooms and season with salt and pepper and sauté them until softened and slightly browned around the edges, about 5 minutes. Remove from heat and set aside.
On a pizza wheel, dusted with semolina (or corn meal), stretch or roll out the pizza into a large round.
Spread the sauce over the dough, leaving about a 1-inch space from the edge of the dough.
Top with the mozzarella cheese and then distribute the soppressata, cooked mushrooms and olives evenly around the pizza.
Brush the outside edge of the dough with olive oil and sprinkle about a 1/2 teaspoon each of the dried basil, oregano and red pepper flakes over the top.
Top with the parmesan cheese.
Carefully slide the pizza from the peel onto the hot stone in the oven and bake for 10 - 15 minutes (depending on the temperature of your oven) until crust is golden brown.
Carefully transfer the pizza to a cutting board and let cool for a few minutes, then slice and serve right away.