The Japanese cooking technique of simmering food in soy sauce, mirin, and dashi is called nimono.
Nimono literally refers to simmered dishes in Japanese cuisine. A main ingredient—often vegetables, fish, seafood, tofu, or meat—is gently cooked in a seasoned liquid called shiru. That liquid commonly includes dashi stock, soy sauce, mirin, and sometimes sake, sugar, salt, miso, or vinegar.
The technique is valued for allowing ingredients to absorb the seasoning while softening gradually. Examples include nikujaga, a beef-and-potato dish; nishime, simmered vegetables; and various fish dishes such as sakana no nimono. The exact ingredients and balance of sweet, salty, and savory flavors vary by region and recipe.
Nimono is a broad category, not one single recipe. Teriyaki also uses soy sauce and often mirin, but it generally involves grilling, broiling, or pan-cooking with a glossy glaze rather than simmering food in a stock. Yakitori is grilled chicken, while tempura is food coated in batter and deep-fried.