Preheat oven to 350 degrees F. Pound chicken breasts to about 1/4 " thick. Lay 2 slices of cheese on each breast, followed by 2 slices of ham and anoother 2 slices of cheese. Leave a 1/2 inch margin on the sides to allow sealing. Roll up each breast like a jelly roll and tuck in the sides. Secure with toothpicks if needed. Combine flour, salt and pepper and spread out on wax paper or a plate. Combine breadcrumbs with salt, pepper, thyme and oil. Beat together water and eggs. Dust the chicken rolls with flour mixture, dip in egg, and then coat with breadcrumb mixture. Place rolls in a baking dish and bake for 20 minutes or until cooked through and browned. Cut into pinwheel slices and serve. Serves 6-8.