Choose the thinnest asparagus you can find, and be sure that the tips are evenly distributed among the packets.
1. Preheat oven to 400°F. Place 4 16-inch lengths of foil on work surface. Fold foil in half from short side. Unfold. Shape corners and edges of one half into semicircular “bowl” with 1/2-inch sides. Coat insides of foil with cooking spray.
2. Place 1 slice of toast in each foil packet. Combine mushrooms, asparagus, and shallots in medium bowl. Add 1/4 cup broth, and season with salt and pepper, if desired. Divide mixture among packets.
3. Whisk together remaining 1 1/2 cups broth, egg, egg white, and thyme in small bowl. Season with salt and pepper, if desired. Drizzle each packet with 1/2 cup broth mixture. Fold other half of foil over ingredients, and crimp edges in overlapping folds until packets are sealed. Transfer packets to baking sheet, and bake 25 to 30 minutes.
4. Transfer to serving plates. Let each person open packet carefully—escaping air will be hot. Sprinkle with chèvre.