For well-browned, crisp chicken skin, heat 1 tablespoon vegetable oil in a large skillet over medium-high heat and brown the chicken, skin side down, before placing on top of the mushrooms.
Position a rack in the center of the oven. Preheat the oven to 400°F. Lightly oil a baking pan or shallow baking dish just large enough to hold the chicken pieces in a single layer.
Place in the bottom of the baking pan:
If using shiitakes, discard the stems or save them for stock. Add to the pan:
Trim any excess fat from:
Season with:
Lay the chicken breasts skin side up on top of the mushroom mixture. Brush lightly with:
Bake, uncovered, until the internal temperature of the chicken reaches 160°F, 35 to 45 minutes.
Using a slotted spoon, transfer the chicken and mushrooms to a platter, arranging the chicken skin side up on the mushrooms. Pour the pan juices into a small saucepan and skim off the fat with a spoon. Add:
Boil over high heat until reduced to about 1 cup or until slightly thickened. Taste and adjust the seasonings. Spoon some of the sauce over the chicken and pass the rest separately. If desired, sprinkle the chicken with: