Preparing the Breast:
Slice each chicken breast from the fat side, almost to the middle. As you near the edge, with about an inch left, open it up. Trim the pointy bottom off and make a series of small, shallow cuts vertically along the fat middle portion. Do not cut through the chicken.
Place in a heavy Ziploc or between two sheets of plastic. Using the fat size of a meat mallet, gently pound chicken to 1/4 inch thickness; when pounding, coax the chicken into something resembling a rectangle. Season with salt and pepper.
Fill and shape the Chicken:
Leaving a half-inch edge around the breast, with a little more space on the long edge furthese away, place two slices of ham. Add grated cheese. Bring the bottom of the chicken towards the ham and cheese, beginning the roll, while bringing the two sides in, folding and rolling. Turn to place the seam at the bottom. If any ham or cheese is sticking out, unroll and poke them in so that when the roll is complete, you have chicken sealed against chicken.
Squeeze the log gently to seal. Lay a piece of plastic wrap down and place your chicken log on the plastic, seam side down, horizontal to the bottom edge of the plastic. Roll the plastic wrap around the chicken, leaving the short sides of the chicken roll open.
Grab a hold of the plastic wrap to the left and right of the chicken, one end in each hand. Firmly roll the chicken on the counter, letting the plastic wrap tighten. Pick it up and roll again several times. The plastic will tighten around the chicken, forcing it into a nicely rounded and uniform shape. Refrigerate for at least an hour and up to overnight – this helps to seal the chicken well.
If you wish to freeze this as a make ahead meal, do so at this point. Thaw overnight in the fridge and continue with the recipe.
Prepare flour, egg wash, and breadcrumbs:
In three dishes of appropriate size for the rolled chicken, prepare the three step breading process. Add flour to one and season with salt and pepper. In the second, beat together eggs and water, the mixture should be fluid. In the third, mix the breadcrumbs with thyme, salt, and pepper. Set out a rack for the breaded chicken.
Lightly dust the chicken with flour, making sure the ends are coated. Pat gently to shake off excess. Dip and roll in the egg mixture, again taking care to coat ends; let excess drain off the roll. Finally, place in the bread crumbs, completely coating. Press gently to adhere. Place on rack and refrigerate for at least an hour for best adhesion.
Bake, Fry, or Deep Fry:
Bake at 350 for about 20 – 25 minutes, deep fry at 350 for about 6 – 8 minutes, or pan fry in about 1/2 inch of oil, four minutes per side. Test for a temperature of 160 to 165 degrees. 165 is the safe temperature for chicken, a short rest, if removed at 160 degrees and lightly covered with foil, should raise the temperature to 165 without overcooking the chicken.
Nutrition:
Per Serving (excluding unknown items): 371 Calories; 20g Fat (48.4% calories from fat); 33g Protein; 14g Carbohydrate; trace Dietary Fiber; 120mg Cholesterol; 420mg Sodium. Exchanges: 1 Grain(Starch); 4 1/2 Lean Meat; 1 Fat.