Preheat oven to 375℉.
Bring a large pot of water to boil.
In a 9x13-inch baking dish, add the garlic, shallot, red pepper flakes, olive oil, wine, lemon zest, salt, pepper, and shrimp. Toss until well combined.
Place into the oven and bake until shrimp is cooked through, about 13 minutes.
Add pasta to the boiling water with plenty of salt (about 1 tablespoon) and cook according to package directions.
Remove the shrimp from the oven and drain the pasta.
Add the pasta to the baking dish with the shrimp and gently toss until coated. Add the parmesan (if using) and toss once more. Taste and add more salt as needed.
Divide among 4 bowls, top with parsley, and serve with lemon wedges.