Preheat the oven to 400°F. If you're using a pizza stone, place it in the oven to preheat. If using a baking sheet, lightly oil it and sprinkle it with a light coating of cornmeal.
Arrange the broccoli florets and mushroom slices separately on a baking sheet (don't mix them), and arrange the bell pepper and onion on a second baking sheet (also separately — don't mix).
Drizzle each type of veggie with a few dashes of olive oil, using about a tablespoon total, or as much as you need to lightly coat them.
Roll the pizza dough to a 14-inch circle. Lightly brush the dough with about 2 tablespoons of olive oil. If you're using a pizza stone, sprinkle it with a light coating of cornmeal. Transfer the dough to the preheated pizza stone or baking sheet. Optionally, sprinkle the top with a bit of cornmeal.
Place the vegetables and pizza crust in the oven (Note 1).
Roast the vegetables until they're tender and lightly browned, about 17 to 20 minutes. Bake the crust until it is puffy and browned, also about 17 to 20 minutes (Note 2).
Sprinkle the vegetables with salt and pepper to taste when they're done.
Spread the hummus over the baked crust, then sprinkle it with fresh basil. Arrange the roasted vegetables over the pizza.
Slice the pizza and serve.