Cook the linguine or spaghetti according to package instructions until al dente. Drain and set aside, reserving 1/2 cup of the pasta water.
In a large skillet, melt the butter and olive oil over medium heat.
Add the minced garlic and red pepper flakes (if using) to the skillet. Sauté for about 1-2 minutes until fragrant, but do not let the garlic brown.
Add the shrimp to the skillet in a single layer. Season with salt and pepper. Cook for about 2-3 minutes on one side until pink, then flip them to cook the other side for another 2-3 minutes.
Once the shrimp are cooked, add the lemon juice, lemon zest, and reserved pasta water to the skillet. Stir gently to combine.
Add the cooked pasta to the skillet and toss everything together until well coated.
Remove from heat, sprinkle with chopped parsley, and adjust seasoning if needed.
Serve immediately, topped with grated Parmesan cheese if desired.