Start a pot of salted water to cook the pasta in a large pot. Cook pasta until just underdone. Reserve about a cup of cooked pasta water, drain the pasta and set aside.
Meanwhile, melt the butter and olive oil in a large shallow pan over medium-high heat.
Add the shrimp to the pan in a single layer and allow to cook undisturbed for 1 minute. Flip, and cook until the shrimp are just cooked through (about 1 minute).
Remove the shrimp from the pan and add the garlic. Saute until fragrant (30 seconds to a minute).
Add the red pesto, sun-dried tomato paste, and chili flakes, stir to combine, and saute to release the flavors (about a minute).
Mix the in the cream, add the stock, the Parmesan cheese, vinegar, a pinch of salt, and freshly ground black pepper. Mix and bring to a simmer. If the sauce is too thick, add a small amount of reserved pasta water. Simmer for 3 to 5 minutes to bring the flavors together.
Add the pasta to the sauce, and simmer gently to allow the pasta to finish cooking in the sauce. If the sauce is too thick, add a small amount of reserved pasta water. Stir in the cooked shrimp, and mix in the basil.
Taste for seasoning and add more salt as needed before serving.