Bring a large (5 or 6 quarts) pot of water to a boil and season with 3 tablespoons kosher salt.
Cook the pasta according to package directions until al dente (usually about 11 minutes). Scoop 1/2 cup of the pasta water out of the pot and set aside, then drain the pasta and transfer to a bowl.
While the pasta is cooking, pat the shimp with a paper towel to dry them. Sprinkle lightly with salt on both sides.
Put a large (12-inch) skillet over medium-high heat. Pour in the oil. When it starts to shimmer, add the shrimp in one layer. Cook 2 minutes, then turn them over and continue cooking until they turn pink and opaque, about 1 more minute.
Add the tomatoes, garlic, butter and chili to the pan and stir. When the butter is melted, add 2 or 3 tablespoons of the reserved pasta water and swirl around until saucy (add more if needed, a tablespoon at a time).
Pour the shrimp and sauce over the pasta. Top with the parsley and Parmesan cheese to taste. Toss gently and serve. Enjoy!
Squeeze the juice of half a lemon over the finished dish for an extra spark of acid and flavor.