Bring a large pot of lightly salted water to a boil. Cook spaghetti in the boiling water, stirring occasionally, until cooked through but firm to the bite, about 12 minutes; drain. Transfer to a large mixing bowl.
Melt butter with olive oil in a large saucepan over medium-low heat. Cook and stir asparagus, red bell pepper, shallots, garlic, basil, red pepper flakes, and oregano in the butter mixture until the pepper is softened, about 5 minutes. Add shrimp and continue cooking until the shrimp are bright pink on the outside and the meat is no longer transparent in the center, 3 to 5 minutes more.
Pour shrimp and vegetable mixture over the spaghetti and toss to mix. Sprinkle Parmesan cheese over the pasta mixture and season with salt and pepper.
