Have ready:
Trim any fat around the edges. One at a time, place the breasts between sheets of wax paper and pound with a mallet or rolling pin until about ⅜ inch thick. Season both sides with:
Arrange the chicken smooth side down on a work surface. Cover one half of each breast with:
Leaving space around the edges, top the ham slice with:
Fold each chicken breast in half over the ham and cheese and press the edges firmly together to seal. Combine in a wide shallow bowl:
Whisk together in a shallow bowl:
Spread on a plate:
Press both sides of each packet in the flour, then dip in the egg mixture, then coat with the bread crumb mixture, patting with your fingers to make the crumbs adhere. Set aside on a plate. Heat in a large heavy skillet over medium-high heat until shimmering:
Place the packets in the skillet and cook until browned on both sides, 3 to 4 minutes each. Drain on paper towels and serve immediately.