After cooking your meat or fish, take it out of the pan. Do not clean the pan--the little brown bits left in the pan will be the base of your sauce. Pour out all but 2 tablespoons of the fat from the pan (or add some other fat, if needed).
Add the garlic and ginger to the pan and cook over medium heat until aromatic, 1 to 2 minutes. Add the rice vinegar and soy sauce and use a wooden spoon to scrape up the browned bits from the bottom of the pan. Simmer until the liquid has thickened and reduced by half.
Add the mirin and simmer to reduce until the sauce is thickened; swirl in the sesame oil. Add the scallions and stir to combine.
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