Put all the ☆ ingredients into a pan, and add the ginger slices if you like. Bring to a boil. (The photos shows the pan before the ginger is added.)
Put the mackerel in the boiling cooking liquid and put on a small lid or piece of kitchen parchment paper that sits right on top of the food (otoshibuta). Simmer for about 20 minutes.
Set the heat to about medium, just so that the pan doesn't boil over. When the liquid has reduced to about 1/3, it's done. Watch the pan so that the fish doesn't burn...
Please also see Recipe ID: 1423112, "Sardines Simmered With Umebosh".
Also see Recipe ID: 1322732, "Simmered Halibut".
Also see Recipe ID: 1367324, "Simmered Sandfish".
Story Behind this Recipe
I like mackerel simmered in soy sauce rather than miso. When I used to work full time in an office, I loved the 'mackerel set lunch' offered at a local restaurant. I recreated the flavor of their simmered mackerel.
If you add the mackerel after the cooking liquid has come to a boil, it won't be fishy. Reduce the cooking liquid to about 1/3. I always feel like the fish haven't been seasoned enough whenever I don't cook down the sauce.