How to Make It
Preheat the oven to 400°. In a small bowl, combine 1 1/2 tablespoons of the miso with the garlic, ginger and honey.
Pat the chicken breasts dry with paper towels. Using your fingers, make a small opening in each breast between the meat and skin (be careful not to break the skin). Stuff a quarter of the miso paste through each opening and press lightly on the skin to work the paste all over the breasts. Lightly season both sides of the chicken with salt and pepper.
Heat the vegetable oil in a large skillet. Add the chicken breasts to the pan, skin side down, and cook over moderately high heat until brown and crusty, about 4 minutes. Turn and cook on the other side until brown and crusty, about 3 minutes. Transfer the chicken to a baking sheet and bake for about 15 minutes, or until cooked through.
Pour off the fat from the skillet. Add the scallions to the skillet and cook over high heat until fragrant, about 1 minute. Pour in the chicken stock and scrape the bottom of the pan with a wooden spoon to loosen the browned bits. Cook over high heat until the sauce has reduced to 1/2 cup, about 12 minutes. Whisk in the remaining 1 tablespoon miso. Strain the sauce through a fine-meshed sieve, pressing on the solids. Stir in the basil and season with salt and pepper.
To serve, transfer the chicken breasts to plates and spoon the pan sauce on top.