Flatten chicken breasts to 1/8-in. thickness; spread butter on the insides. Sprinkle with thyme. Top with a slice of ham and cheese; roll up tightly. Wrap each with 2 slices of bacon and secure with toothpicks.
In a small bowl, beat eggs and milk. Place flour in another bowl. Combine the bread crumbs, garlic powder, oregano and cheese. Dip each chicken breast into egg mixture; dip into flour to coat. Dip each again into egg mixture, then coat with crumbs.
Place on a greased baking sheet. Bake, uncovered, at 350° for 40-45 minutes or until chicken juices run clear.