Pound chicken to ¼” thick. Season with salt and pepper to taste.
Top each chicken breast with 1 slice of ham and about 1 oz cheese.
Roll the chicken jelly roll style. Secure with a toothpick.
Combine butter and garlic in a small dish. Mix breadcrumbs and thyme in a separate bowl. Dip each chicken roll in butter and then into the breadcrumb mixture.
Place in a baking dish and bake 35-40 minutes or until chicken reaches 165°F.