Put the mirin in a saucepan over high heat and bring to a boil. Lower the heat and simmer for 5-6 minutes.
Add the sugar and stir until melted. Add the soy sauce and heat up slowly over medium-low heat, stirring several times, until the surface is barely bubbling. It should not boil vigorously or the flavor of the soy sauce will dissipate. Simmer gently for 5 minutes, skimming off any white scum that forms on the surface.
Let cool and store in a glass jar or other nonreactive, airtight container. The kaeshi can be used immediately but is better if rested for at least a day. Store in the refrigerator or other cool, dark, place. It will keep for several months.