Bring a large pot of salted water to a boil. Cook the pasta until al dente. Before draining, reserve at least ½ cup of the pasta cooking water. Drain the pasta and set aside.
Pat the shrimp dry and season with salt and pepper.
In a large skillet, heat the butter and olive oil over medium-high heat. Add the shrimp in a single layer and cook for 1–2 minutes per side, just until pink and opaque. Transfer the shrimp to a plate and set aside.
Reduce the heat to medium. Add the minced garlic to the same skillet and cook for about 30 seconds, stirring constantly, just until fragrant. Do not let the garlic brown.
Add the white wine and simmer for 2–3 minutes, scraping up any browned bits from the bottom of the skillet.
Stir in the heavy cream and cook for 1–2 minutes, until the sauce is slightly thickened.
Stir in the lemon zest, 1 tablespoon fresh lemon juice, and most of the chopped parsley and basil, reserving some for garnish.
Add the cooked pasta and a small splash of the reserved pasta water. Toss well, adding more pasta water a little at a time, as needed, until the sauce lightly coats the pasta.
Return the shrimp to the skillet and toss gently until heated through, about 30 seconds to 1 minute.
Taste and adjust the seasoning with additional salt and pepper, if needed. Serve immediately, garnished with the remaining parsley and basil.