Preheat a pizza stone measuring 14 to 16 inches in diameter in an oven set to 500°F.
Prepare one unbaked pizza crust of the same size. Lightly brush the surface of the crust with 1 tablespoon of olive oil. Take half of the blackberries and mash them, then spread the smashed berries evenly over the crust.
Evenly sprinkle 1 cup of shredded mozzarella cheese and 1 cup of shredded Parmesan cheese on top.
Slice the remaining blackberries in half and scatter them across the pizza. Add heaping teaspoon-sized dollops of ricotta cheese, spacing them out randomly across the surface.
Bake the pizza directly on the preheated stone for 10 to 15 minutes, or until the cheese is bubbling and begins to brown.
While the pizza bakes, roughly chop or chiffonade 10 large fresh basil leaves. Add the basil to the pizza during the final few minutes of baking.
Once done, remove the pizza from the oven and cut into 8 large slices.