Get the ingredients you want to use together (See Helpful Hints for more.) If you want to keep the sauce for a long time, sterilize the storage container properly.
Put the mirin and sake in a pan and heat over low-medium to evaporate the alcohol. If you want to concentrate the flavors, simmer for a while.
(If the steam rising from the pan no longer smells like alcohol, it's good.) If you are making a large amount, measure out the soy sauce while the pan is simmering.
When the alcohol has evaporated, add soy sauce. I used dark soy sauce this time, but it's fine to use whatever type of soy sauce you prefer. Bring the pan back to a boil, then turn off the heat.
Add powdered dashi base of your choice (such as powdered bonito flakes or powdered dried sardines) and it's done! (If you add the dashi right away, the sauce may boil up suddenly, so cool the sauce down a bit before adding the granules).
To store the sauce, let it cool down before transferring to a container, then refrigerate (If there is any sediment in the sauce that bothers you, strain the sauce through cloth first.)
This is a 2-3 times concentrate mentsuyu sauce. If you are concerned that the sauce loses flavor and fragrance over time, don't make it in advance, but just make it fresh every time you need it.
If you use shiro-shoyu, you can make shiro-dashi. Strain dashi stock sediment for a clear sauce.
You can use the basic mentsuyu sauce and add sugar and other things to it to turn it into tentsuyu (tempura dipping sauce). I also recommend a saltier version with less mirin.
Story Behind this Recipe
The pickier I got about the flavoring ingredients I used, the more I felt like making my own mentsuyu and shiro-dashi - and so I do now. Of course, the better the basic ingredients, the better your mentsuyu or shiro-dashi will be. But in any case, you can make it easily with familiar ingredients, so give it a try even if you're a novice cook.
You can make this with mirin flavored seasoning, but hon-mirin is best. The powdered dashi base can be dried bonito, dried kombu seaweed, dried sardines or whatever you like! If you can get it, use ago-dashi, which is made from flying fish... it will make your sauce totally delicious.