Cut each chicken breast into thin cutlets. You will get 2 or 3 per piece depending on their thickness.
In a shallow dish combine pork rinds, parmesan cheese, salt, and pepper. In a separate shallow pan combine the beaten egg and heavy whipping cream. Mix well.
Place chicken breasts one at a time first in the egg cream mixture and then the pork rind breading mixture.
Heat extra virgin olive oil in a skillet or frying pan on medium heat. Next place chicken breasts in the heated skillet. Allow the chicken to sear well before turning them over. This will take about 4 to 6 minutes per side.
Transfer the browned chicken to a large rimmed baking sheet.
Sauce
Meanwhile, add the butter, cream cheese, and heavy cream to a small saucepan.
Heat over medium heat, whisking, until the cream cheese has melted and the sauce is smooth. Season with salt and pepper.
Assembly
Add the chicken to a large rimmed baking sheet.
Spoon the sauce over the browned chicken breasts. Top with the cheddar cheese.
Bake in a preheated oven at 350 for 5-10 minutes until the chicken reaches 160.
Optional: Broil for 1-2 minutes to brown the cheese.
Notes
Pork Rind Crumbs - You can buy these prepared or just put regular unflavored pork rinds in a food processor or blender until they are fine crumbs.