Bring a large pot of heavily salted water to a rolling boil. Pat the peeled and deveined shrimp completely dry on both sides with paper towels, which removes surface moisture to ensure a quick sear rather than steaming. Season the shrimp lightly with salt and black pepper.

Melt 1 tablespoon of the unsalted butter with 1 tablespoon of the olive oil in a large skillet over medium-high heat. Once the fat begins to shimmer, lay the shrimp in a single layer and sear undisturbed for 60 to 90 seconds per side just until they turn pink and opaque. Immediately transfer the shrimp to a clean plate; do not overcook them at this stage, as they will finish warming in the sauce later.

Drop the spaghetti into the boiling water and cook it for exactly 2 minutes less than the package instructions indicate for al dente. This ensures the pasta remains firm enough to finish its final cooking stage directly inside the skillet sauce without becoming mushy.

Reduce the skillet heat to medium and add 3 tablespoons of the butter along with the remaining 2 tablespoons of olive oil. Drop in the minced garlic and red pepper flakes, sautéing for 60 seconds while stirring constantly until fragrant. Watch closely to prevent the garlic from taking on color or scorching, which creates a bitter taste.

Pour the dry white wine into the skillet, using a wooden spoon to aggressively scrape up any caramelized savory bits stuck to the bottom of the pan. Bring the liquid to a rapid simmer and let it reduce by half, cooking off the harsh alcohol vapors and concentrating the fruit acids.

Right before draining the pasta, ladle out and reserve exactly ½ cup of the cloudy, boiling pasta water. Drain the spaghetti and add it directly to the simmering wine and garlic base.

Pour in the lemon juice, lemon zest, the final 1 tablespoon of cold butter, and ¼ cup of the reserved starchy pasta water. Increase the skillet heat to medium-high and toss the pasta continuously with tongs for 2 minutes. As the starches from the water combine with the melting butter and oil under high heat, they form a glossy, unified cream-like emulsion.

Slide the seared shrimp and any collected plate juices back into the bubbling skillet, tossing for 60 seconds until the seafood is heated through and completely coated in the silky garlic-butter sauce. Fold in the fresh chopped parsley, adjust with additional salt or pasta water if the sauce appears too thick, and serve immediately.