In a large skillet, melt the butter with the olive oil over medium heat. Add the mushrooms and salt and cook, stirring occasionally, until the mushrooms are tender and well-browned (about 8 minutes). Add the broth and cheese and bring to simmer while stirring. Let simmer until slightly thickened.
Snap the tough ends from the asparagus and cut the spears into 1/2-inch pieces. In a large boiling pot of salted water, cook the pasta until almost done (about 8 minutes). Then add the asparagus and cook until the pasta is done (an additional 4 minutes).
Drain the pasta and asparagus. Toss with the mushrooms and sauce.