Preheat oven to 350F. Place asparagus in a shallow roasting pan. Coat with about 1 tablespoon of oil and sprinkle with a little salt and pepper. Roast until done, about 20 minutes.
Meanwhile, heat water for pasta.
Heat 1 tablespoon olive oil in a large skillet over medium-high heat. Add onion and mushrooms, cook 5 minutes or until they are tender.
Add thyme and garlic, cook 1 minute. Sprinkle mixture with the flour and stir to coat. Cook for 30 seconds to cook the flour. Stir in the broth and half and half, cook until thickened, about 2 minutes.
Put the pasta in to cook (11 minutes). Retain about a 1/2 cup of liquid to you if you want to thin the sauce a little.
Add the peas, 2 tablespoons of cheese, lemon rind, lemon juice, salt and pepper.
Once the pasta is done, drain, add the sauce and gently fold in the roasted asparagus. Top with the rest of the Parmesan cheese.