Set an inverted baking sheet on a rack in the center of the oven and preheat the oven to 450 degrees F. Invert another baking sheet and place a piece of parchment on top and set aside.
Melt the butter in a small saucepan over medium heat. Stir in the garlic and crushed red pepper flakes, and cook until fragrant, about 2 minutes. Pour in the wine and reduce until the alcohol smell is no longer present and the sauce is golden, 4 to 5 minutes. Remove the pan from the heat and stir in the lemon zest. Season with salt and pepper and set aside.
Dust the parchment paper on top of the inverted baking sheet with flour. On a lightly floured work surface, roll out and stretch the dough into a 12-inch circle then place it on the paper. Scatter the shrimp evenly over the dough leaving a 1/2 inch border all around. Spoon the butter sauce over the shrimp, and use a pastry brush to spread the sauce to the edges. Finish by sprinkling the mozzarella cheese over the top, staying within the border.
Place the sheet pan with the pizza on top of the preheated inverted baking sheet and bake until the dough is crisp and the shrimp are cooked through, 12 to 14 minutes. Sprinkle the pizza with the parsley and freshly grated Parmesan, slice into wedges and serve immediately.