Do this one often. Ok cast iron folks give it a try. I brine the breast overnight. Next day I coat them with salt, pepper and some Italian rub. Fire up the Weber and I use the vortex ring for this placed in the center. I'll add a small piece of cherry wood on coals and place the breast on the outside of the grate away from heat. I'll let the breast go for about 20 minutes, just to get some smoke flavor on them. While this is going on I make my reduction.
https://www.acouplecooks.com/balsamic-reduction/
And grill up the mushrooms. When the mushrooms are done I place a cast iron pan over the fire and coat with olive oil. When the pan gets hot I'll add the chicken breast to get a good crust to them. As they are about to be done I add butter, garlic, shallots to the pan to make a nice pan sauce. Keep basting the chicken with the sauce until the chicken is done. Place the chicken on a platter and spoon sauce over the chicken. Next dice up the mushrooms and pour them over breast. Coat with the reduction sauce and enjoy. Goes with just about any side but is very good with roasted smash potatoes