1. Pound the chicken breasts evenly across the surface, using plastic wrap or parchment paper to prevent sticking.
2. Heat oil and butter in a cast iron skillet or frying pan over medium heat.
3. In three separate bowls, add flour to one, buttermilk and egg mixture to the second, and breadcrumbs with seasonings to the third.
4. Pat dry each piece of chicken, then dip into flour, buttermilk mixture, and finally breadcrumb mixture.
5. Add chicken (3 at a time) to the hot skillet and fry for approximately 6-8 minutes per side until golden brown.
6. Remove and place on a plate lined with paper towels. Repeat with remaining chicken.
7. Place cooked chicken on a baking sheet, top each with Swiss cheese, ham, and another slice of Swiss.
8. Bake at 350° until cheese melts, about 5 minutes. Carefully remove from the oven.
9. For the dipping sauce, mix mayonnaise, Dijon mustard, yellow mustard, and honey in a small bowl.