Preheat an outdoor grill or indoor grill pan to medium heat - approximately 200 degrees Fahrenheit.
In a large bowl, toss the prepared veggies with the olive oil, salt, and pepper.
Grill the veggies just until grill marks are formed on each side. Do not overcook the veggies, because they will cook more in the oven. You want the veggies to blister and get those nice grill marks without being overcooked.
Once the veggies have been grilled, remove them to a large platter and allow them to cool while you prepare the sauce and the dough.
Fill a metal mixing bowl with hot tap water and set aside for a few minutes. This will temper the bowl and help to ensure the yeast will properly activate.
Pour the hot water out of the bowl and wipe the bowl dry. Add the warm tap water and the yeast. Using a rubber spatula, gently stir the yeast into the water for no more than 5-10 seconds. Set aside and let the yeast bubble and foam for at least 3 minutes.
Sift together the flour, salt, and sugar. Stir in the cheese.
Add the olive oil to the yeast and water mixture. Stir for a few seconds. Pour in the entire flour mixture and stir with a rubber spatula until the liquid is absorbed.
Sprinkle your clean counter top with a little flour and empty the dough out. Knead the dough together for 4-5 minutes until a dough ball is formed. Place the dough back into the metal mixing bowl, cover with a tea towel, and set the bowl aside. Let the dough sit for five minutes.
While the dough is proofing, prepare the sauce by adding the oil, garlic, dried basil and dried oregano to a bowl. Whisk together. Set aside. Next, prepare a pizza pan, pizza stone, or a large baking sheet by brushing it with a little olive oil. Set aside. Also, preheat your oven to 500 degrees.
When the dough is ready, sprinkle a clean counter top with a little flour and roll the dough into a 1/4 inch round. Aim for a 15 inch flat pizza round. Transfer the rolled dough to the prepared pan.
Smear the entire surface of the pizza dough with the olive oil and garlic sauce mixture. Use a pastry brush for this.
Top the pizza with 1 1/2 cups of the cheese, followed by the peppers, zucchini, onion, and tomatoes.
Top with the remaining 1/2 cup cheese.
Bake for 12 minutes.
Remove from oven and sprinkle the top with the fresh chopped basil, dried red chili flakes, and parmesan cheese. Drizzle over the olive oil and cut into 8 slices. Serve immediately.