In a large Dutch oven, heat oil over medium. Add garlic and ginger and cook, stirring, until fragrant, 30 seconds. Add mushrooms, onion, soy sauce, mirin, sugar and ¼ cup of water.
Season chicken with salt and pepper and add to the pot. Mix well and bring to a boil over medium-high. Cover, reduce heat to low and cook for 15 minutes. Stir in potatoes and bring back to a simmer. Cover and cook over low heat until potatoes are almost tender, 10 to 15 minutes. Uncover and cook, stirring occasionally, until chicken and potatoes are cooked through and sauce is reduced and slightly thickened, 10 to 15 minutes longer. Stir in scallions.
Divide chicken mixture among shallow bowls and garnish with scallions and sesame seeds, if using. Serve warm, with rice and kimchi on the side.
