Preheat the oven to 375º. Place a wire rack inside a rimmed baking sheet.
In a shallow bowl, combine the panko, canola oil, salt, and pepper. Set aside.
Pat chicken breasts dry with paper towel. Using a sharp knife butterfly each chicken breast, leaving one long side attached. Open each chicken piece like a book with the cut side facing up. Lay a sheet of plastic wrap or parchment on top and pound to an even ¼-inch thickness with a mallet.
With the cut-side facing up, cover with an even layer of Swiss cheese. Arrange ham slices over the cheese. Roll up each chicken piece like your would a swiss roll and secure the seam with toothpicks.
Place the flour into a shallow dish. Place the eggs into a separate shallow dish. Dredge stuffed chicken breasts, one at a time, in the flour, shaking off any excess. Coat the chicken in egg mixture, then place into panko mixture turning to coat.
Arrange the chicken breasts on the wire rack, seam side down.
Bake for 35 to 45 minutes or until golden brown.