Sprinkle chicken with 1/4 t pepper and salt. Combine cheeses in a bowl. And the remaining 1/4 t pepper, breadcrumbs, parsley and 2 t oil in another bowl.
Heat the remaining oil in a large ovenproof nonstick skillet over medium heat. Cook the chicken until browned on both sides, about 2 minutes per side. Move the chicken to the center so all pieces are touching. Spread with cheese mixture, sprinkle with ham, then top with breadcrumb mixture.
Bake until the chicken is no longer pink and registers 165F internally, 5-7 minutes.