Bring a large pot of heavily salted water to a boil. Add linguine and cook according to package directions until al dente. Reserve 1 cup of pasta water before draining.

While pasta cooks, melt 3 tablespoons of butter in a large skillet over medium-high heat. Add garlic and red pepper flakes and cook for 30 seconds until fragrant. Add the shrimp and cook for 1-2 minutes per side until pink. Remove shrimp from the skillet.

Pour the white wine into the skillet and scrape up any browned bits. Let it simmer and reduce by half. Reduce heat to low, then add the remaining 3 tablespoons of butter, lemon juice, and lemon zest. Swirl the pan until the butter is melted and the sauce is smooth. Stir in 1/4 cup of reserved pasta water.

Add the drained pasta to the skillet and toss to coat. Return the shrimp to the pan along with the fresh parsley and Parmesan cheese. Toss to combine everything. Serve immediately.