Preheat your oven to 375°F. You’re gonna finish off the rolls for a nice crisp.
Place chicken breasts between two sheets of plastic wrap. Pound them down to about ¼-inch thickness.
Layer each breast with one ham slice and one Swiss cheese slice. Roll up tight and secure with toothpicks.
Season flour with salt and pepper in a shallow dish. Dredge each roll in the flour, dip in eggs, then coat with breadcrumbs.
Heat oil and butter in a skillet over medium heat. Brown chicken rolls on all sides for about 4-5 minutes.
Transfer rolls to a baking dish and bake for 25–30 minutes in the oven.
Remove toothpicks before serving.
Serve hot with your choice of sides.
Store leftovers in foil or airtight container in fridge for up to 3 days or freeze for up to 2 months.
To reheat, thaw in fridge overnight and bake in oven to retain crisp texture.
Notes
Use toothpicks to keep rolls secure during cooking. Natural pressure release helps maintain juicy texture. You can use mozzarella or provolone instead of Swiss cheese.