i've made this a few times recently with some success, using a whole quartered chicken, but it works with just breasts as well. it's my version of chicken murphy.
first, remove the skin from the breasts, rinse, pat dry and dredge in s&p seasoned flour. in a skillet, combine a few tbsps of butter and olive oil, and brown the chicken over medium high heat, meat side down first. when you flip them onto the bone side, toss in a handful of fresh sage leaves and 2 cups of large diced chorizo or linguica. sear for a few minutes more, then set aside.
in the same skillet, add a little more olive oil and butter, and quickly brown 1/2 inch eggplant rounds that were also dredged in seasoned flour. do not cook them through, just a quick sear. set eggplant aside. deglaze the pan with a cup of white wine, and reserve the liquid.
in a bowl, toss 1/2 inch slices of bell peppers and red onions, and whole shiitake caps in evoo and s&p. place mix in a layer on the bottom of a large glass baking dish.
nestle the browned chicken breasts into the pepper/onion/shiitake mix, and spread the chorizo and sage around the dish. place the eggplant rounds around the chicken. pour the reserved white wine deglazing over top of everything. if necessary, add a little chicken stock so that you can see a little layer of liquid along the bottom.
next, slice small red potatoes into thin, 1/8 inch slices, toss in evoo and s&p, and spread over top of most of the dish, creating a kind of potato blanket.
put into 400 degree oven for 30 minutes, then turn up the heat to 450 until the potatoes turn brown and crispy.
plate the veggies, chicken, chorizo, and potatoes, and reduce the remaining liquid to make a sauce.