Make the sauce: In a small bowl, whisk together the soy sauce, rice wine (mirin), sesame oil, and brown sugar. Set aside.
Sauté aromatics: Heat a wok or large skillet over medium-high heat. Add the peanut oil, then stir in the garlic and ginger. Cook, stirring constantly, until fragrant and lightly golden, about 30 seconds.
Brown the chicken: Add the chicken pieces and stir-fry until browned on all sides, about 3 to 5 minutes.
Add the sauce: Pour the sauce over the chicken and continue cooking, stirring occasionally, until the chicken is cooked through and the sauce begins to reduce, about 8 to 10 minutes.
Thicken if needed: If the sauce hasn’t thickened to a syrupy consistency, stir together 1 tablespoon of cornstarch with 1 tablespoon of cold water in a small bowl. Pour the slurry into the pan and stir until the sauce thickens and coats the chicken, 1 to 2 minutes.
Finish and serve: Add the dried red peppers and green onions. Stir to combine and cook for 1 more minute, then serve hot over rice.