Place a plastic wrap over a flat surface. Arrange a piece of chicken over the wrap, and then cover the chicken with it. Pound the chicken using a meat tenderizer tool until it flattens.
Sprinkle salt all over the chicken breast.
Prepare the filling by putting a slice of cheese and ham over the chicken. Roll the chicken to cover the filling and then seal it by inserting toothpicks into the rolled chicken.
Heat oil in a cooking pot.
Dip the chicken in beaten egg and then roll over the bread crumbs. Do this step twice to make the coating thicker.
Deep fry for 12 minutes in medium heat. Note. if you need to turn the chicken over to fry the opposite side, you can do so and cook it for 8 minutes. If you will deep while the chicken is fully submerged, 12 minutes should be enough, but feel free to cook no longer than 15 minutes.
Remove the chicken from the pot. Let it cool down. Slice into serving pieces.
Prepare the sauce by melting butter in a sauce pan. Add onion. Cook until soft.
Pour heavy whipping cream. Let boil. Add Dijon mustard. Stir and continue to cook in medium heat until it reduces to half. Add salt to taste.
Pour sauce over the chicken. Serve.
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