In a large pot of boiling salted water, cook the linguine according to package instructions until al dente. Reserve about 1/2 cup of pasta water, then drain and set aside.
In a large skillet over medium heat, melt the butter. Once melted, add the minced garlic and red pepper flakes, sautéing for about 1-2 minutes until fragrant but not burned.
Add the shrimp to the skillet, seasoning with salt and pepper. Cook for about 2-3 minutes on one side until they turn pink, then flip them over and cook for another 1-2 minutes until fully cooked and opaque.
Stir in the lemon zest and lemon juice, then add the cooked pasta to the skillet. If the mixture seems dry, add the reserved pasta water a little at a time until the desired consistency is reached. Toss everything together well until the pasta is fully coated.
Remove from heat, taste, and adjust the seasoning with additional salt and pepper if necessary.
Plate the shrimp scampi, garnishing with fresh parsley and sprinkling with grated Parmesan cheese if desired. Serve immediately.