Bring a saucepan of water to a boil over medium heat and very lightly boil the bok choy for 3 minutes. Drain and refresh in cold water and set aside.
Place the miso, scallions, ginger, and garlic in a bowl. Stir in the honey and soy sauce. Add the chicken and stir to coat it well. Leave to marinate in the fridge for a minimum of 30 minutes, or ideally overnight.
Preheat the broiler or a heat a cast-iron grill pan over high heat. Broil the chicken for about 15 minutes, turning halfway through. Add the bok choy and broil for an additional 5 minutes. Check that the chicken is cooked by cutting open a piece in the thickest part and making sure there is no pink meat inside.