Heat a 12-inch sauté pan over medium-high and melt 1 tablespoon of the butter.
Add the shrimp, season with salt and freshly ground black pepper, and cook, stirring occasionally, until opaque and cooked through, about 2–4 minutes depending on size.
Transfer the cooked shrimp to a piece of foil, wrap to keep warm, and set aside.
Return the pan to medium heat and melt the remaining 2 tablespoons butter.
Add the minced garlic and sauté about 20 seconds until fragrant and just beginning to color.
Pour in 3 cups water and 1 cup half-and-half, then add the 12 oz linguine; season with salt and pepper to taste and bring to a boil over medium-high heat.
Boil, stirring frequently, until the pasta reaches your desired doneness, about 8–10 minutes; some liquid should remain in the pan to form the sauce.
Remove the pan from heat and stir in the shredded Parmesan until it melts into a creamy sauce; if the sauce is too thick, thin with additional half-and-half.
Toss the reserved shrimp back into the pan to warm through, then sprinkle with chopped parsley and serve warm.
