1. Combine 5 cups water, bacon, and shiitake mushrooms in a saucepan; cover. Bring to a boil; remove from heat. Let stand, covered, 15 minutes. Strain through a fine-mesh sieve over a bowl; discard solids. Return broth to saucepan; stir in soy sauce. Keep warm.
2. Bring remaining 2 cups water to a simmer in a Dutch oven. Place eggs in a vegetable steamer. Place steamer in pan over water; cover. Reduce heat to medium-low. Steam eggs, covered, 6 minutes. Add bok choy to steamer; steam 2 minutes. Set bok choy aside; place eggs in a bowl of ice water. Let eggs stand 1 minute or until slightly cool. Peel and halve eggs.
3. Divide noodles evenly among 4 deep bowls. Top evenly with bok choy, enoki mushrooms, and bamboo shoots. Ladle 1 cup warm broth into each bowl. Arrange nori around edges of bowls. Place 2 egg halves in center of each bowl; top evenly with green onions. Serve immediately.