Preseason chicken and shrimps. In a small bowl, mix chicken pieces with 1/2 tsp soy sauce and 1/2 tsp Mirin. In another bowl, mix shrimp and 1/2 tsp soy sauce and 1/2 tsp Sake. Let them sit for a couple of minutes.
Meanwhile, in a large bowl, mix eggs, Dashi, salt, 1 tsp soy sauce, and Mirin together. Strain the egg mixture through a sieve. Let as much egg as you can go through the sieve.
Place 1/4 amount of chicken, shrimp, and shiitake mushrooms in each of 4 small cups (such as ramekins), then pour egg mixture over them to fill 3/4 of a cup. Cover with aluminum foil and put the covered cups into a steamer.
Steam at medium heat for 10-15 minutes. Check with a wooden skewer to see if it's done. If clear broth comes out when poked, take the cups out from the steamer.