Lay a large layer of sliced ham on a clean work surface, then roll the block of cheddar cheese up in it.
Make a butterfly cut in both turkey breasts, then unfold them next to one another on your clean work surface. Season the turkey breasts with salt and pepper, then snugly roll the ham & cheese filling up inside the turkey. For the best results, wrap the whole thing up in plastic wrap, transfer it to the refrigerator, and let it chill for 6 hours so that it will stay together better during the next steps.
Preheat the oven to 300°F, heat a large pan filled with cooking oil on the stove, and set up the breading with separate dishes for the whisked eggs, flour, and bread crumbs. Remove the stuffed turkey breast from the refrigerator and remove the plastic wrap, then dredge it in egg wash, coat it in flour, and cover it in bread crumbs. Briefly fry the breaded turkey on all sides in hot cooking oil.
Place the fried turkey cordon bleu on a baking tray, transfer the baking tray to the oven, and bake at 300°F for 2–2½ hours. Use a meat thermometer to check the internal temperature, and when it reaches 150°F, remove the turkey cordon bleu from the oven. To serve, top everything off with a creamy white sauce and chopped parsley.
