Bring a large pot of generously salted water to a boil. Cook pappardelle pasta just before al dente. Strain and set aside.
Meanwhile, remove the tails from the shrimp and pat dry with a paper towel.
Heat oil in a large pan over medium heat. Once hot, add shrimp and season with salt and pepper. Cook for 1 minute per side. Add a splash of additional oil along with shallot, garlic, and tomatoes. You want enough oil in the skillet so the garlic doesn't stick to the pan. Season with a big pinch of salt. Cook for 1 minute, shaking the pan so the tomatoes cook evenly.
Add wine and parsley and simmer for 1 more minute.
Add heavy cream and lime juice and stir. Bring back to a gentle simmer. Cook until slightly thickened, about 2 minutes.
Fold in pappardelle and toss to coat in the sauce. Let simmer for an additional 2-3 minutes, tossing periodically until the cream is thickened and sticks to the pasta.
Serve immediately topped with additional chopped parsley.
Notes
The recipe calls for heavy/whipping cream because it has a high enough fat content to not curdle/separate in the hot pan. Heavy cream can be boiled and simmered, unlike lighter creams. light cream or half and half will not yield the same results.