Bring a large pot of salted water to a boil. Cook the linguine according to package directions until al dente. Reserve 1 cup of pasta water before draining.

While the pasta cooks, pat the shrimp dry with paper towels and season with salt and pepper on both sides.

Heat 1 tablespoon of butter and the olive oil in a large skillet over medium-high heat. Add the shrimp in a single layer and cook for 2-3 minutes per side until pink and cooked through. Transfer to a plate and set aside.

Reduce heat to medium and add the remaining 3 tablespoons of butter to the same skillet. Once melted, add the minced garlic and red pepper flakes. Sauté for 30-60 seconds until fragrant, stirring constantly to prevent burning.

Pour in the white wine and add the lemon zest. Let it simmer for 2 minutes, scraping up any browned bits from the bottom of the pan.

Add the drained pasta to the skillet and toss to coat in the sauce. Add 1/4 cup of the reserved pasta water and toss again. Add more pasta water as needed to create a silky sauce that coats the pasta.

Remove the skillet from heat. Add the cooked shrimp, lemon juice, and chopped parsley. Toss everything together gently. Taste and adjust seasoning with salt and pepper as needed. Serve immediately topped with freshly grated Parmesan cheese.