Place the flour into a wide, flat bowl and season with salt and pepper to taste. Mix to combine the seasoning and then set the bowl to one side.
Using a sharp knife, cut both of the chicken breasts horizontally most of the way through, stopping just short of cutting them in half.
Open the chicken breasts out into a heart shape, cover them with plastic wrap and then, using a heavy rolling pin or a mallet, gently flatten the chicken until it is roughly ⅓ inch thick.
Remove and dispose of the plastic wrap, and place a slice of ham, a slice of cheese, and two sage leaves onto one half of each chicken breast. Fold one half of the chicken breasts over the other half and press down lightly.
Break the egg and whisk it gently with a fork, and place into a wide, flat bowl. Place the breadcrumbs into another wide, flat bowl.
Taking one chicken breast at a time, coat with the seasoned flour, and then coat in the egg mixture, then finally cover thoroughly with breadcrumbs.
In a large frying pan, gently heat up the butter until it is melted and lightly foaming. Place the chicken breasts into the pan and allow them to gently cook on one side for 7 minutes, before turning and cooking for another 7 minutes on the other side. The cordon bleu are ready when the chicken is cooked through and the cheese has melted.
Once ready, remove the cordon bleu from the pan and allow to sit for a few minutes before serving.