Preheat the oven to 400F
Make the basil pesto by adding the ingredients in a blender and blending until creamy, adding water if needed.
In a small pan over medium heat, add 1 tablespoon olive oil. Add the mushrooms, and cook for about 5 minutes, occasionally stirring until the mushrooms are tender. Remove from heat and set aside.
In a mixing bowl, toss the squash and zucchini with 1 tablespoon olive oil and a pinch of salt and pepper.
Next, assemble the pizza by topping the crust with basil pesto, squash, zucchini, and mushrooms. Place into the oven and bake for 10-15 minutes.
Remove the pizza from the oven and top with small dollops of the pesto, fresh basil leaves, red pepper flakes, vegan parmesan, and a drizzle of olive oil.