Preheat oven to 450°F. Let it preheat with a pizza stone or overturned baking sheet in it.
To make the crust, combine flour, baking powder, and salt in a large bowl or food processor. Add olive oil and water, 1 tablespoon at a time, mixing or pulsing until the dough starts to come together. Knead the dough a few times, if needed, to form a ball. Let dough rest for 10 to 15 minutes while preparing cheese and toppings.
Add white cheddar cheese, swiss cheese, and provolone cheese to a food processor and pulse until crumbled or use a box grater to grate each type of cheese and toss to combine.
Prepare any pizza toppings by slicing veggies and cooking meat, if using.
Divide the ball of pizza dough in half and roll out on a piece of parchment paper until very thin, about ⅛".
Spread half of the pizza sauce evenly over each pizza all the way to the edges. Sprinkle with a generous amount of the cheese, reserving some cheese for sprinkling on top of the other toppings.
Top with your favorite pizza toppings or the cooked bacon, sausage, green peppers, red onion, and mushrooms used here for the deluxe version. Sprinkle with any reserved cheese.
Slide the parchment paper onto the hot pizza stone or overturned baking sheet in the preheated oven and bake for 10-12 minutes or until the crust is crispy and the cheese is starting to brown.
Cut into squares with a pizza cutter and serve.