Preheat your oven to 350°F (175°C).
Pound chicken breasts to an even thickness using a meat mallet.
Place a slice of ham and a slice of cheese on each chicken breast.
Roll up each chicken breast tightly and secure with toothpicks.
Dredge each rolled chicken breast in flour, followed by egg, and then coat in breadcrumbs.
Heat olive oil in a skillet over medium heat. Sear the chicken rolls until golden brown on all sides.
Transfer the seared chicken rolls to a baking dish and bake in the preheated oven for 20-25 minutes, or until cooked through.
Once done, remove toothpicks, slice, and serve warm. Season with salt and pepper to taste.