Bring 4 cups water, the ginger, and kombu to a boil in a large, wide pot. Reduce heat and simmer, covered, 4 minutes. Turn off heat, sprinkle in bonito flakes, and let sit 3 minutes (flakes will sink). Strain broth through a cheesecloth-lined fine-mesh strainer into a bowl.
Rinse pot, then pour in broth. Add leek and carrots. Bring to a simmer and cook 2 minutes. Add black cod and scallops; simmer 1 minute. Add shrimp and cook 2 minutes more.
Whisk miso with lager in a small bowl. Remove stew from heat and carefully stir in miso mixture. Serve with lemon zest and shiso for topping if you like.
*Find kombu, a large seaweed sold dried, and bonito flakes with the Asian ingredients at well-stocked supermarkets and at natural-foods or Japanese markets. Find shiso, an aromatic herb, at Japanese markets and some farmers' markets.
Note: Nutritional analysis is per serving.