Coat and cook the chicken. While the sweet potatoes continue to cook, on a plate, combine the flour and half the cheese; season with salt and pepper. Pat the chicken dry with paper towels; season both sides with salt and pepper. Working 1 piece at a time, thoroughly coat the chicken in the flour-cheese mixture (tapping off any excess). In a large pan (nonstick, if you have one), heat a thin layer of oil on medium until hot. Once hot enough that a pinch of flour sizzles immediately when added, add the coated chicken. Cook 4 to 6 minutes per side, or until golden brown and cooked through. Transfer to a paper towel-lined plate; immediately season with salt and pepper.