For the chicken: For each chicken breast, carefully remove the skin and the tenderloin (the small strip of meat on the inside) and set the tenderloin aside. Slice the breast horizontally, but don't cut all the way through—leave one side attached so you can open it like a book. Once opened, place a piece of parchment paper over the chicken and gently pound it with a saucepan or similar tool to flatten it. Do the same with the tenderloin: slice it down the middle without cutting all the way through, open it, and flatten it.

On one half of the chicken breast, place a piece of sheep's milk cheese, a piece of cooked ham, and another piece of cheese.

Fold the other half of the chicken breast over the filling (so it's closed) and use the tenderloin to cover and seal the filling inside the chicken. Repeat with the second chicken breast.

Place the flour, breadcrumbs, and beaten eggs (seasoned with salt and pepper) in separate shallow dishes. Carefully dip each stuffed chicken breast first in flour, then in egg, and finally in breadcrumbs.

Heat a skillet over low heat with a little oil and the butter. Gently place the cordon bleus in the pan and cook for a few minutes on each side until golden. Handle carefully so the filling doesn't spill out.