Bring a large pot of salted water to a boil and cook the angel hair pasta according to package directions (about 4 minutes); before draining, reserve 1/2 cup of the pasta cooking water, then drain the pasta.
While the pasta cooks, heat the olive oil and butter in a large skillet over medium-high heat until the butter is melted and hot.
Add the shrimp to the skillet, season with salt and freshly ground black pepper, and sauté about 2 minutes.
Add the minced garlic to the skillet and cook, stirring, until the shrimp are cooked through, about 2 more minutes.
Toss the drained pasta into the skillet with the shrimp. Add 1/3 cup of the reserved pasta water, the lemon zest, and the lemon juice; toss to combine, adding additional reserved pasta water 1 tablespoon at a time if the sauce seems dry.
Stir in 2 tablespoons each of the chopped parsley and chopped basil, then remove from heat and sprinkle with the shredded Parmesan and the remaining 1 tablespoon each of parsley and basil; toss gently to combine.
Serve the pasta warm.