Preheat your oven to 375°F. Prepare a baking sheet by lining it with parchment paper.
Place each chicken breast between two sheets of plastic wrap and pound them to about 1/2 inch thick using a meat mallet or rolling pin.
Season both sides of the chicken breasts with salt, pepper, garlic powder, onion powder, and paprika.
Lay 2 slices of ham and 2 slices of Swiss cheese on each chicken breast. Roll the chicken tightly, starting from one end, and secure with toothpicks or kitchen twine.
Set up a breading station: Place the flour in one shallow dish, beat the eggs in another dish, and combine the breadcrumbs with a pinch of salt and pepper in a third dish.
Dredge each chicken roll in flour, shaking off excess, then dip into the beaten eggs, and finally coat with breadcrumbs, pressing gently to adhere.
In a large skillet, heat the vegetable oil over medium heat. Once hot, carefully add the chicken rolls and cook for about 4-5 minutes on each side until golden brown.
Transfer the browned chicken to the prepared baking sheet and bake in the preheated oven for 15-20 minutes, or until the internal temperature reaches 165°F.
While the chicken is baking, prepare the Dijon sauce by mixing sour cream, Dijon mustard, lemon juice, salt, and pepper in a small bowl until smooth.
Once the chicken is done, let it rest for a few minutes before slicing. Serve with the Dijon sauce drizzled on top or on the side.