In a shallow baking dish, whisk together the soy sauce, brown sugar, sesame oil, and ginger; stir in the 2-inch scallion pieces and the star anise, if using. Season the chicken with salt and add to the marinade, turning to coat. Let marinate at room temperature for 30 minutes.
Line a footed metal colander with 2 layers of damp cheesecloth, allowing 2 inches of overhang. Place in a pot and add enough water to just reach the colander bottom. Bring to a simmer; have a small pot of boiling water on the side.
Pour the couscous into the colander. Place the chicken thighs on top in a single layer, pressing up the sides of the colander, if necessary; reserve the marinade. Cover and steam, adding more hot water as needed until the chicken is cooked through, 25 to 30 minutes.
Meanwhile, in a small saucepan, simmer the reserved marinade until thickened, about 4 minutes; strain.
When the chicken is almost done, scatter the bok choy on top, season with salt and steam for 3 minutes. Transfer the bok choy and chicken to a platter, drizzle with the marinade and top with half of the sliced scallions. Stir the remaining scallions into the couscous, season with salt and serve with the chicken.