Put a pizza stone or an inverted baking sheet on the middle oven rack and preheat to 450 degrees F. Press and stretch the pizza dough into a 10-by-14-inch rectangle on a floured piece of parchment; scatter the shallot on top. Drizzle with 1 tablespoon olive oil and rub into the dough, gently pressing in the shallot; season with salt and pepper. Transfer the dough (on the parchment) onto the hot stone. Bake until the crust is golden, 10 to 15 minutes.
Meanwhile, bring the wine, 1 tablespoon olive oil and the garlic to a simmer in a large skillet over medium heat. Add the clams, cover and cook until they open, about 6 minutes; transfer to a cutting board using a slotted spoon. (Discard any unopened clams.) Continue simmering the liquid until reduced by half, 2 to 3 minutes. Remove the clams from their shells and chop.
Pulse the parsley with the remaining 2 tablespoons olive oil and the lemon zest in a mini food processor until chopped. Add the clam cooking liquid (with the garlic) and pulse until thickened.
Spread the parsley sauce on the baked crust. Top with the clams and shrimp; lightly season with salt and pepper. Return to the oven until the shrimp is cooked through, 3 to 5 minutes. Top with more parsley.