Add onion and mushrooms; saut 5 minutes or until tender.
Add thyme and garlic; saut 1 minute.
Sprinkle mushroom mixture evenly with flour; cook 30 seconds, stirring constantly. Stir in broth and half-and-half; cook 2 minutes or until slightly thickened.
Add peas, 2 tablespoons cheese, rind, and next 3 ingredients (through pepper); cook 1 minute or until peas are thoroughly heated.
Cook pasta according to package directions, omitting salt and fat. During the last 3 minutes of cooking, add asparagus to pan; drain.
Add pasta mixture to mushroom mixture; toss gently to coat.