How to Make It
Place 1 1/2 cups cold water and kombu in a small saucepan; heat over high until steaming. Remove from heat; sprinkle katsuobushi over broth, and steep 3 minutes. Strain dashi into a bowl; discard solids.
Process remaining 1/2 cup water and chopped ginger in a blender until smooth, about 1 minute. Pour ginger water through a fine wire-mesh strainer; discard solids.
Preheat oven to 450°F. Combine rinsed rice, 1 cup dashi, ginger water, sake, and salt in a 3-quart donabe or lidded saucepan, and cover. Cook over low until beginning to boil, about 8 minutes. Cook, checking rice often, until liquid is evenly boiling over the whole surface, about 7 minutes. Immediately place donabe in preheated oven, and bake until rice is tender, about 15 minutes. Remove from oven, and let rest, covered, 5 minutes.
Meanwhile, bring brown sugar, soy sauce, garlic, and grated ginger to a boil in a small saucepan over medium-low. Boil until sauce thickens to a syrup consistency, about 5 minutes. Let cool, and reserve.
Place one-fourth of the cooked rice (about 1 cup) in each of 4 cedar steamer baskets (wappa). Top evenly with crab and avocado. Working 1 basket at a time, place basket over simmering water; cover and cook until rice and toppings are heated through, about 4 minutes. Remove from heat. (Alternatively, divide rice among warmed bowls, and top with crab and avocado.) Top evenly with cucumber, roe, nori, and sesame seeds, and serve immediately with sweet soy glaze.