Preheat the oven to 400°F (200°C). If you plan to use a pizza stone or steel, place it in the oven now so it heats while the oven preheats; otherwise line a baking sheet with parchment paper.
Unfold the thawed puff pastry shell on a lightly floured surface or on the parchment paper. Gently press or roll it out just enough to smooth seams and make an even shape; keep the overall size close to the original shell.
Using the tip of a knife, score a 1/2-inch border all the way around the pastry without cutting through it. This will create a raised edge when baked.
Transfer the pastry (on the parchment) to the prepared baking sheet, or keep it on the parchment for transfer onto the preheated pizza stone/steel.
Spread 1/4 cup BBQ sauce evenly over the pastry inside the scored border.
Sprinkle half of the mozzarella (1/4 cup) evenly over the sauce.
Arrange the roasted, sliced cauliflower evenly over the cheese. Evenly scatter the 3 tablespoons corn, 3 tablespoons petite black beans, 3 tablespoons chopped red pepper, and 3 tablespoons chopped green pepper over the cauliflower.
Sprinkle the remaining mozzarella (1/4 cup) over the top of the arranged toppings.
Bake on the baking sheet, or slide the parchment with the pizza onto the preheated pizza stone/steel, for 15–22 minutes, until the puff pastry is golden brown and the edges are puffed.
Remove from the oven, let the pizza rest for 3–5 minutes, then slice and serve.