Sprinkle chicken with 1/4 teaspoon pepper and salt. Combine Gruyère cheese and cream cheese in a bowl. In a separate bowl, combine the remaining 1/4 teaspoon pepper with breadcrumbs, parsley (or thyme) and 2 teaspoons oil.
Heat the remaining 2 teaspoons 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 centre so all pieces are touching. Spread with the cheese mixture, sprinkle with ham, then top with the breadcrumb mixture.
Place the ovenproof skillet in the oven; bake until the chicken is no longer pink in the centre and an instant-read thermometer registers 165°F, 5 to 7 minutes.
Tip: one whole chicken breast might be too large for individual portions so removing the tenders (the soft strip from the underside of a 5 to 6 ounce breast) will reduce the breast by about 1 ounce. Freeze the tenders and use them for another dish.