Set up the steamer: fill a wide pot with 1 to 1 1/2 inches of water, bring to a boil, then lower to the gentlest simmer. Set out four heatproof cups of about 3/4 cup (180 ml) each.
Lightly season the chicken pieces with a tiny pinch of salt and a few drops of the soy sauce from the custard measure. Leave the shrimp plain.
Whisk the eggs gently with chopsticks or a fork using a cutting, back-and-forth motion, with no foam on top.
Stir the cooled dashi, soy sauce, mirin, and salt into the eggs until just combined. The dashi must feel no warmer than lukewarm.
Strain the mixture through a fine-mesh strainer into a clean jug to remove chalazae, shell bits, and foam.
Divide the chicken, shrimp, shiitake, and kamaboko among the cups. Pour the strained egg mixture over, filling each cup about 3/4 full, lay spinach or mitsuba leaves on top, skim any bubbles, and cover each cup with a lid, foil, or plastic wrap.
Steam the cups in the simmering water (about halfway up their sides) with the pot lid slightly ajar for 12 to 15 minutes, keeping the water barely moving, never at a hard boil.
The custard is done when the surface looks set and glossy and the cup trembles gently when tapped, and a skewer comes out with clear liquid. Serve hot with small spoons, topped with zest if using.