Begin by cooking the pasta according to package instructions in a pot of boiling salted water until al dente. Reserve ½ cup of the pasta cooking water, then drain the pasta in a colander and set aside.
While the pasta cooks, heat the butter and olive oil in a large skillet over medium heat. Once melted, add in the minced garlic and red pepper flakes. Sauté for about 1-2 minutes until the garlic is fragrant and lightly golden.
Add the shrimp to the skillet and season with salt and pepper. Cook for 2-3 minutes until the shrimp turn pink and opaque, stirring occasionally.
Pour in the white wine or chicken broth, scraping any browned bits from the bottom of the skillet. Allow the mixture to simmer for about 2 minutes.
Stir in the lemon juice and half of the reserved pasta water. Add more pasta water if the sauce seems too thick, until the desired consistency is reached.
Add the cooked pasta directly into the skillet with the shrimp and sauce. Toss everything together until well combined, allowing the pasta to soak in the flavors.
Remove the skillet from heat, sprinkle with chopped parsley, and give it a final toss. Adjust seasoning with salt and pepper if needed.
Serve immediately with grated Parmesan cheese, if desired.