Pound and assemble: Place each chicken breast between two sheets of plastic wrap and pound to an even ½-inch thickness. Lay 2 slices of ham and 1 slice of Swiss on top of each piece, then fold or roll the chicken around the filling, securing with a toothpick if needed.
Chill the assembled chicken before breading don’t skip this: Place the assembled chicken on a plate or tray and freeze for 15 minutes. This short chill firms up the chicken and filling so the ham and cheese stay put instead of oozing out through the seams during baking breading warm, unchilled chicken often leads to melted cheese escaping before the crust has time to set and seal everything in.
Set up the breading station: While the chicken chills, set up three shallow dishes: one with flour, one with the beaten eggs, and one with the panko mixed with garlic powder, paprika, salt, and pepper.
Preheat the oven to 400°F and set a wire rack inside a rimmed baking sheet.
Bread the chicken: Dredge each chilled chicken piece in flour, shaking off the excess, then dip in the egg, and finally press firmly into the panko mixture until fully coated on all sides.
Bake on the rack, not directly on the pan: Place the breaded chicken on the wire rack and lightly spray or drizzle with oil. Baking on a rack instead of directly on the sheet lets hot air circulate underneath the chicken, so the bottom crisps up the same way the top does chicken baked flat on a pan traps steam against the bottom, which is exactly what leaves that side soggy no matter how crispy the top gets.
Bake until golden: Bake for 22–25 minutes, until the coating is deep golden brown and the internal temperature reaches 165°F. Let rest for 3–4 minutes before slicing.
Make the sauce and serve: While the chicken bakes, whisk together the mayonnaise, Dijon mustard, honey, and lemon juice for the honey mustard sauce.