Make the white sauce: In a medium saucepan, melt the butter over medium heat. Add the flour and whisk to combine. Cook, whisking frequently, until the roux turns golden brown and begins to smell nutty, about 3 minutes. Slowly whisk in the milk and cook, continuing to whisk constantly, until the sauce begins to bubble and thicken, about 3 minutes. Add the Pecorino-Romano and whisk to incorporate until completely melted. Remove the pot from the heat, cover, and set aside.
Make the seafood: In a large, high-walled skillet, heat the olive oil over medium heat. Add the garlic and Calabrian chiles and cook until the garlic begins to turn golden and smells toasty, about 3 minutes. Add the salt, then carefully pour in the wine and bring to a boil. Add the mussels and clams and cook until the shellfish begin to open, about 3 minutes. Add the shrimp and continue cooking until they turn bright pink, about 3 minutes more. Remove the clams, mussels, and shrimp from the pan using a slotted spoon, leaving the broth behind. Remove the clam and mussel meat from the shells and set aside with the shrimp, discarding the shells. Cover the broth and keep warm until ready to serve.
Assemble the pizza: Pour 1 tablespoon olive oil onto a baking sheet and use your fingers to spread evenly. Place the pizza dough on the baking sheet and drizzle the remaining 2 tablespoons of olive oil over the dough. Use your fingers to press the dough into a 12-inch-wide circle, creating a 1-inch wide lip around the edges and pressing more firmly in the center of the dough to flatten into a well. Fill the well with white sauce, then top with the clams, mussels, and shrimp.
Bake until the sauce is bubbling and the crust is a very dark brown with some extra-crispy bits around the edges, about 10 minutes. Remove the pizza from the oven and transfer to a large cutting board.
While still hot, grate Parmigiano-Reggiano cheese all over the pizza, then top with the parsley. Slice the pizza.
Pour the seafood broth into a small bowl and serve alongside the pizza with lemon wedges for squeezing.