In a large measuring cup or bowl, combine the mirin, soy sauce, and sugar. Set it aside.
Heat a Dutch oven or stockpot over medium-high heat and add the oil. When it is hot, add the onions, garlic, and ginger and stir-fry for about 3 minutes until it is fragrant and the onions are softening.
Add the chicken and cook it until it is no longer pink on the outsides, 3 – 5 minutes, then add the carrots and potatoes and stir to combine.
Add the mirin mixture and ½ cup of water, bring it to a boil, then cover, reduce the heat to low, and simmer it for 15 – 20 minutes, stirring once or twice, until the potatoes are fork tender. Serve it immediately or refrigerate it for up to 3 days.
Omit the oil. Combine the mirin, soy sauce, sugar, and ½ cup of water in the slow cooker, then add the remaining ingredients. Cook on low for 8 - 10 hours or high for 4 - 5 hours. (Slow cooker cooking times may vary—Get to know your slow cooker and, if necessary, adjust cooking times accordingly.)
