How to Make It
In a medium saucepan, combine the chicken stock with the soy sauce, sugar, mirin and sake and bring to a boil over high heat, stirring to dissolve the sugar. Reduce the heat to moderate and simmer until the teriyaki sauce is reduced to 1/2 cup and syrupy, about 20 minutes.
Meanwhile, season the chicken with salt and pepper. In a large nonstick skillet, heat 1 tablespoon of the oil. Add the chicken and cook over moderately high heat, turning once, until browned all over and cooked through, 8 to 9 minutes. Transfer the chicken to a plate and let stand for 5 minutes.
Wipe out the skillet. Add the remaining 1 tablespoon of oil and heat until shimmering. Add the pepper strips and cook over high heat, stirring occasionally, until crisp-tender and lightly charred, about 3 minutes. Transfer the peppers to plates. Slice the chicken breasts crosswise and transfer to the plates. Drizzle the teriyaki sauce over the chicken and serve with rice.