Bring a large pot of salted water to a rolling boil and cook linguine until al dente; reserve 1 cup of starchy pasta water before draining.

Pat shrimp dry with paper towels to ensure a good sear, then season both sides with salt and pepper.

Melt 4 tablespoons of butter and 2 tablespoons of oil in a large skillet over medium heat until fragrant and shimmering.

Sear shrimp in a single layer for 1-2 minutes per side until pink, opaque, and curled, then remove and set aside.

Add remaining butter and oil to the skillet, then sauté garlic and red pepper flakes for 1 minute until fragrant and golden.

Pour in the wine or broth to deglaze the pan, simmering for 2 minutes to reduce the liquid by half.

Stir in lemon juice and lemon zest to create a bright, citrusy sauce.

Return shrimp to the skillet and cook for 2 minutes, basting them in the sauce until glistening.

Toss the cooked pasta into the skillet, adding reserved pasta water as needed to achieve a silky, glossy coating.

Remove from heat, stir in fresh parsley and half the Parmesan cheese until creamy, then garnish and serve immediately.