Serve sprinkled with chopped fresh parsley. This pizza is inspired by a similar pie at Pizzeria Regina in Boston's North End.
Adjust oven rack to lowest position and heat oven to 500 degrees. Cook 3 tablespoons oil, garlic, anchovies, ¼ teaspoon pepper, and pepper flakes in small saucepan over medium heat, whisking to break up anchovies, until garlic just begins to turn straw-colored, about 4 minutes. Transfer to bowl and let cool. Pat shrimp dry with paper towels and toss with salt, 1 tablespoon oil, and remaining ¼ teaspoon pepper.
Brush rimmed baking sheet with remaining 1 tablespoon oil. Press and roll dough into 15 by 11-inch rectangle on lightly floured counter. Transfer dough to prepared sheet. Spread garlic oil over dough. Layer spinach over pizza. Sprinkle with Pecorino, followed by mozzarella. Scatter shrimp over cheese.
Bake until edges and underside of crust are well browned and shrimp are cooked through, 12 to 16 minutes, rotating sheet halfway through baking. Transfer pizza to wire rack and let cool for 5 minutes. Serve with extra pepper flakes.
