In a small bowl, whisk together the miso, honey, soy sauce, vinegar, ginger, garlic, chile-garlic sauce, 1 tablespoon of the oil and 1 tablespoon water. Refrigerate half of the mixture to use as a sauce for serving.
Place the chicken in a large, shallow dish or resealable plastic bag and pour the remaining miso-honey mixture over the top. Toss the chicken until coated and cover the dish, or seal the bag and turn a few times to coat. Marinate the chicken in the refrigerator for up to 30 minutes. (Marinating longer may dry out the chicken.)
When you're ready to cook, heat the broiler with a rack about 6 inches from the heat source. Line a large sheet pan with foil.
Remove the chicken from the marinade, scraping off and discarding any excess. Place the chicken, flatter side up, in a single layer on one side of the pan. Place the asparagus on the other side. Drizzle the asparagus with the remaining 2 teaspoons oil, then season with salt and pepper, toss to coat and spread in a single layer.
Broil until the chicken is cooked through with some charred spots and the asparagus is browned, about 10 minutes.
To serve, drizzle the chicken with the reserved miso-honey and sprinkle with the scallions. Serve with rice, if desired.
