In a large pot of salted boiling water, cook the linguine or spaghetti according to package instructions until al dente. Drain and set aside, reserving 1 cup of pasta water.
Season the shrimp with salt and pepper.
In a large skillet over medium heat, melt the butter. Add the minced garlic and red pepper flakes, sautéing for about 1 minute until fragrant, being careful not to burn the garlic.
Increase heat to medium-high and add the shrimp to the skillet. Cook for 2-3 minutes until they turn pink, stirring frequently.
Pour in the chicken broth and heavy cream, stirring to combine. Let the mixture simmer for about 2 minutes to thicken slightly.
Stir in the lemon zest and juice, mixing well. If the sauce is too thick, add reserved pasta water a little at a time to reach your desired consistency.
Add the cooked pasta to the skillet, tossing well to coat in the garlic butter sauce. Use tongs to mix gently, ensuring the shrimp and sauce evenly coat the pasta.
Remove from heat and stir in the fresh parsley. Adjust seasoning with more salt and pepper if needed.
Plate the shrimp scampi hot, garnishing with grated Parmesan cheese on top.
Notes
Adjust seasoning to taste and add more pasta water if the sauce is too thick.