Using a small, sharp knife, carefully make an incision along the side of each chicken breast to create a pocket without cutting all the way through.
2 boneless, skinless chicken breast
Season the ham with salt and pepper. Wrap each slice around a piece of Swiss cheese, then insert it into the pocket in each chicken breast.
2 slice deli ham, kosher salt, black pepper, 2 ounce Swiss cheese
Fold the edges of the chicken together to seal the pocket, making sure no filling is exposed.
Place each breast on plastic wrap and tightly wrap it into a cylinder. Twist and tie the ends, then refrigerate for two hours.
Preheat the oven to 350°F (180°C). Remove the chicken from the refrigerator and discard the plastic wrap.
Arrange the flour, beaten eggs, and panko breadcrumbs in three separate shallow bowls. Season each with salt and pepper.
½ cup all-purpose flour, 2 large egg, 1 cup panko breadcrumbs
Coat each chicken breast in the flour, followed by the egg and then the breadcrumbs. Repeat the breading process for a thick, even coating.
Let the breaded chicken rest for 10 minutes to help the coating adhere.
Heat the neutral oil in a medium frying pan over medium heat.
¼ cup neutral oil
Once the oil is hot but not smoking, carefully add the chicken.
Add the butter and cook, using tongs to continually turn the chicken, until the breading is golden brown all over.
¼ cup unsalted butter
Transfer the chicken to a wire rack set over a baking sheet. Bake for 10-15 minutes, or until the thickest part of the chicken, not the filling, reaches 160°F (71°C).
Rest for five minutes before serving.