In a medium-sized pan, heat the olive over medium heat.
Add the garlic and cook until softened, about 2 minutes.
Add the remaining ingredients and simmer for 15 minutes. Remove from heat and let cool while you prep the toppings.
Preheat 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.
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, mushrooms, and olives evenly around the pizza.
Brush the outside edge of the dough with olive oil and sprinkle a few pinches of 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 8 to 10 minutes (depending on the temperature of your oven) until the 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.
