Have the biscuits ready to slip into the oven to bake as you begin to prepare the chicken. Cut the chicken into 1/2-inch-wide strips. Slice the mushrooms, and if you are using shiitakes, discard the stems. Heat the butter in a skillet; when it stops foaming, add the chicken and mushrooms and saute over moderate heat for 4 minutes. Add the peppers and cook, stirring, over high heat for 1 more minute.
Pour the cream into the skillet and cook until it has reduced and thickened, about 5 minutes. Season with salt and pepper. To serve, split 4 warm biscuits and divide them between 2 plates. Cover them with the creamed chicken.