Fill a large pot with salted water and bring to a rolling boil. Cook linguine according to package instructions until al dente (usually 8–10 minutes). Reserve 1/2 cup pasta water, then drain and set aside.

While the pasta cooks, pat the shrimp dry and season lightly with salt and pepper.

In a large skillet over medium heat, melt 2 tablespoons of butter with 1 tablespoon of olive oil. When shimmering, add the shrimp in a single layer. Cook 2–3 minutes per side until pink and opaque. Remove shrimp to a plate and cover loosely.

In the same skillet, reduce heat to medium-low and add the remaining 2 tablespoons of butter. Add the minced garlic (and chopped shallot if using) and sauté 30–45 seconds until fragrant — do not let it brown. Add red pepper flakes and smoked paprika if using.

Pour in the white wine or chicken broth and simmer 1–2 minutes to reduce slightly, scraping up any browned bits. Add lemon zest and lemon juice.

Add the cooked linguine to the skillet along with 1/3 cup reserved pasta water. Toss well to combine and create a glossy sauce. If the sauce seems dry, add more pasta water, a tablespoon at a time.

Return shrimp to the pan, add chopped parsley, and toss gently until everything is warmed through (about 1 minute). Taste and adjust salt and pepper.

Serve immediately with a generous sprinkle of grated Parmesan and extra parsley. Enjoy hot.