Springtime Sushi Nests

Name: Springtime Sushi Nests
Ingredients: 1 cup Dashi; 1 tablespoon sugar; 4 teaspoons mirin (sweet Japanese rice wine); 1 carrot, peeled, cut into matchstick-size strips; 1/2 cup canned sliced bamboo shoots, cut into matchstick-size strips; 2 large dried shiitake mushrooms, soaked in hot water 30 minutes, drained, stems trimmed, caps thinly sliced; 2 teaspoons reduced-sodium soy sauce; 1 large egg; Pinch of salt; Nonstick vegetable oil spray; 6 asparagus spears, trimmed, cut into 1 3/4-inch pieces; Sushi Rice; 6 butter lettuce leaves; 12 cooked large shrimp, peeled; 1/4 cup shredded red pickled ginger (beni shoga)