To make dashi stock, bring water to a bowl over high heat. Add the dashi stock base and mix well. Lower heat to medium and let simmer for 5 minutes. Remove from heat and let the stock cool to room temperature.
In a bowl, beat eggs until runny and the egg whites are well mixed. Take about 1/2 cup of the beaten egg and transfer to a large mixing bowl. The rest of the eggs will not be used and can be preserved in the fridge for other uses. Add the dashi stock to the bowl containing 1/2 cup of eggs and mix well using a whisk. Season with soy sauce.
Fill 5 small ramekins evenly with the mushrooms, shrimps, and green onions. Pour the egg and dashi stock mixture into each ramekin and cover each ramekin with aluminum foil. Steam over medium high heat for 15-18 minutes, or until the egg custards are firm and fully cooked.