1. Heat a large skillet over medium-high heat. Add oil; swirl to coat. Add onion and mushrooms; sauté 5 minutes or until tender. Add thyme and garlic; sauté 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.
2. 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. Sprinkle with remaining 1 tablespoon cheese.