Cook pasta according to package directions. Drain and return to pot.
Meanwhile, heat oil in a large frying pan over medium-high heat. Cook onion, garlic, and mushrooms until fragrant, about 2 minutes. Add prosciutto and asparagus and cook until asparagus is bright green, about 2 minutes. Add cream, 1/4 cup cheese, the pepper, and chile flakes. Reduce heat to simmer and cook until sauce has thickened, about 4 minutes.
Pour sauce with vegetables over pasta and toss to coat. Serve with more parmesan.