Preheat oven to 400°F (200°C). If using a pizza stone or steel, place it in the oven now to heat while the oven preheats. Ensure the puff pastry shell is thawed according to package directions.
Prepare a work surface and lay a sheet of parchment paper large enough to hold the pastry. If using a baking sheet instead of a stone, line the baking sheet with parchment.
Unfold the thawed puff pastry onto the parchment and gently flatten it out to an even thickness. With the tip of a knife, lightly score a 1/2-inch border all the way around the pastry—do not cut through the pastry so the border can puff.
Spread 1/4 cup BBQ sauce evenly inside the scored border, leaving the border sauce-free.
Sprinkle 1/4 cup of the shredded Mozzarella cheese evenly over the sauce (half of the 1/2 cup).
Arrange the roasted, sliced cauliflower over the cheese, then evenly distribute the 3 tablespoons corn, 3 tablespoons petite black beans, 3 tablespoons chopped red pepper, and 3 tablespoons chopped green pepper across the pizza.
Sprinkle the remaining 1/4 cup shredded Mozzarella cheese over the top.
Transfer the pizza (on the parchment) to the oven: place the parchment with the pizza on the prepared baking sheet, or slide the parchment with the pizza directly onto the preheated pizza stone/steel. Bake 15–22 minutes, or until the puff pastry is golden brown and cooked through.
Remove the pizza from the oven, let rest for a few minutes, then slice and serve.