Preheat your oven to 500°F (260°C) with a pizza stone inside.
In a skillet, melt butter with olive oil over medium heat. Add garlic and red pepper flakes, cooking until fragrant (about 1–2 minutes). Set aside to cool slightly.
Roll out the pizza dough on a floured surface to your desired thickness.
Transfer the dough to a floured pizza peel.
Brush the dough generously with the garlic butter mixture.
Sprinkle half of the mozzarella cheese evenly over the base.
Arrange cooked shrimp evenly on top of the cheese.