Place chicken thighs between two sheets of plastic wrap and pound until 1/2-inch-thick with a meat mallet or a rolling pin. Remove plastic and set aside.
Combine garlic powder, onion powder, and cajun seasoning (for a little kick!) in a small bowl. Season the pounded chicken, first with the salt and pepper, and then with the spice mix. Make sure it is evenly coated with seasoning.
Take chicken thigh and layer with two slices of ham wrapped around two slices of Swiss cheese. Roll the chicken and place onto a new sheet of plastic wrap. Wrap the chicken roll firmly. Repeat steps for remaining chicken and refrigerate for about 30 minutes.
Prepare a breading set up:o One dish for flour, one dish for egg, and one dish for breadcrumbs. Dredge each chicken roll with this sequence: Flour - egg - flour - egg - breadcrumbs. Add more flour or breadcrumbs if you feel like there’s not enough.
Preheat deep cast iron skillet with about 2 inches of oil (vegetable oil is best for this recipe). Shallow fry the breaded chicken on medium-high heat for about 5 minutes or until golden brown. Check the internal temperature by inserting a thermometer. If it reads 165°F, it is done and ready to serve. If not, transfer the browned chicken to a sheet pan with a wire rack and place in a 325°F oven for about 10 minutes or until an internal temperature of 165°F is reached. When done, set the chicken rolls aside to rest.