In a large pot of rapidly boiling, lightly salted water, cook pasta until barely tener, 3-5 minutes. Drain well.
Slice asparagus into small pieces on an angle. Trim stems and slice mushrooms crosswise into umbrella shapes.
In large skillet, melt butter in oil over med-high heat. Heating oil and butter give good favor and keeps butter from burning. Add asparagus, mushrooms, basil, and garlic. Cook, tossing, until asparagus is crisp-tender and mushrooms have softened, about 5 minutes.
Add vegetable broth and bring to simmer. Add pasta, parmesan, salt, and pepper to skillet. Toss gently.