Cook the spaghetti or linguine according to package instructions until al dente. Drain and set aside, reserving 1/2 cup of the pasta water.
In a large skillet, heat the olive oil over medium heat. Add the minced garlic and red pepper flakes (if using) and sauté for about 1 minute until fragrant.
Add the shrimp to the skillet, season with salt and pepper, and cook for 2-3 minutes until they turn pink and opaque.
Pour in the chicken broth, lemon zest, and lemon juice. Stir to combine and let it simmer for 2-3 minutes.
Add the cooked pasta to the skillet, tossing to coat in the sauce. If the pasta seems dry, add reserved pasta water a little at a time until you reach the desired consistency.
Stir in the chopped parsley and adjust seasoning if necessary.
Serve immediately, topped with grated Parmesan cheese.