Heat a 12-inch sauté pan over medium-high heat and melt 1 tablespoon of the butter.
Add the shrimp, season with salt and pepper, and cook, stirring occasionally, until the shrimp are opaque and cooked through, about 2–4 minutes depending on size.
Transfer the cooked shrimp to a piece of foil and wrap to keep warm while you finish the pasta.
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 the water, 1 cup half and half, and add the linguine; season with salt and pepper. Increase heat to medium-high and bring to a boil.
Boil, stirring frequently, until the linguine is cooked to your desired doneness, about 10 minutes; there should still be some liquid remaining for the sauce.
Remove the pan from the heat and stir in the shredded Parmesan until it melts into a creamy sauce; thin with additional half and half if the sauce is too thick.
Toss the cooked shrimp back into the pan to combine and heat through, then sprinkle with chopped parsley and serve warm.