In a large skillet on medium/high heat, sauté asparagus and mushrooms in olive oil until tender. Season with salt and pepper, then remove from the skillet and set aside.
In a medium pot, bring chicken broth (plus 1 cup of water if using 16 ounces pasta) to a boil. Cook pasta until tender. There will be liquid remaining when tender. Do not drain.
While the pasta cook, in the skillet used to sauté the vegetables, melt butter on medium-low heat. Sauté garlic until lightly browned, about 1 minute.
Add milk and stir until it simmers. Add 1/2 cup of the parmesan cheese, and stir until smooth.
Transfer the cooked pasta and remaining liquid in the pan to the parmesan garlic sauce. Toss to coat well.
Stir in 1/4-1/2 cup additional parmesan until well blended. Season with salt and pepper to taste.
Optional: Fold the reserved veggies back into the pasta. Serve topped with additional parmesan cheese.