Bring a large pot of well-salted water to a boil. Cook the linguine according to the package directions until al dente, reserve at least 1/2 cup pasta water, and drain.

Pat the shrimp dry and season with approximately 1/4 teaspoon kosher salt and the black pepper. Dry shrimp sear more effectively and release less water into the skillet.

Heat the olive oil and 1 tablespoon butter in a large skillet over medium-high heat. Cook the shrimp in a single layer for about 1–2 minutes per side, until pink and opaque, then transfer them to a plate.

Reduce the skillet heat to medium and add the remaining 3 tablespoons butter. Stir in the minced garlic and cook for 30–60 seconds, just until fragrant without browning it.

Pour in the heavy cream and add the remaining salt and optional Italian seasoning. Simmer gently for 2–4 minutes without allowing the cream to boil vigorously.

Lower the heat and whisk in the Parmesan a little at a time until the cheese melts and the sauce is smooth. Add the drained linguine and toss until the strands are coated.

Thin the Alfredo sauce with reserved pasta water, 1 tablespoon at a time, until it reaches a creamy consistency. Start with a small amount because the sauce should loosen without becoming watery.

Return the shrimp to the skillet and toss gently for about 1 minute, just to warm them through. Stir in the parsley and serve immediately with additional Parmesan and lemon wedges if desired.