Arrange oven racks in the lower and upper thirds of the oven. Heat oven to 475°F.
Heat 2 tablespoons oil in a large nonstick skillet over medium-high heat. Brown the sausage on both sides until almost done, about 3 minutes. Drain on paper towels.
Meanwhile, roll out the dough on a well-floured surface into two 10-by-14-inch rectangles or 12-inch rounds. Transfer to two ungreased baking sheets.
Top the dough with the sausage, zucchini, and peppers. Sprinkle with the thyme, drizzle with the remaining oil, and season with ½ teaspoon salt and ¼ teaspoon pepper.
Bake the pizzas for 15 minutes. Remove from oven and top with the provolone.
Return to oven 2 to 3 minutes until the cheese melts, the edges of the pies are lightly browned, and the sausage is thoroughly cooked.