Start by placing the chicken breasts between plastic wrap. Use a meat tenderizer to gently pound each to about ¼-inch thick. This ensures the chicken cooks evenly and is easy to roll. Pour the seasoned breadcrumbs into one bowl and whisked eggs into another, and set them aside for coating the rolls later.

Lay one slice of ham and one slice of cheese on each flattened chicken breast. Roll the chicken tightly from one end to the other, keeping the filling secure. Use toothpicks if needed to hold the rolls together, but remove them before serving. Ensure the rolls are sealed to avoid any filling spillage during cooking.

Dip the chicken rolls into the whisked eggs, ensuring every side is covered. Then roll them thoroughly in the breadcrumbs. Press the crumbs gently to ensure they adhere well, creating a crispy, golden coating.

Heat a large skillet over medium-high heat with some oil, and brown the chicken rolls on all sides. This step locks in flavor and adds a beautiful crust. Remove the rolls from the skillet once they are evenly golden brown.

Transfer the browned chicken rolls to a greased baking dish. Bake in a preheated oven at 375°F for about 30 minutes. Baking thoroughly cooks the chicken while keeping the crust crispy and golden.

While the chicken is baking, heat milk and butter in a small saucepan over medium heat. Gradually add the cheese slices, stirring constantly until fully melted and smooth. This luscious sauce is the key to making the dish extra indulgent.

Once the chicken rolls are done baking, drizzle the warm cheese sauce over the top. Plate them alongside your favorite sides, and serve immediately while the cheese is still melty. Watch everyone savor each bite with joy!