Simple Chicken Cordon Bleu

This is my current favorite. Sounds fancy, but very simple. My little picky eaters like it, too. I haven't had great luck getting the sauce to thicken up, but it tastes really good, so nobody seems to mind if it's a bit runny.

Simple Chicken Cordon Bleu

4 skinless, boneless chicken breasts
4 slices Swiss or Provolone cheese
4 thin slices smoked ham
1/4 cup flour
1 egg, beaten
1 cup Italian seasoned bread crumbs
4 tbs. butter
1/2 cup chicken broth
1 cup whipping cream
oregano, garlic, salt and pepper to taste

Pound chicken breast to 1/4-inch thickness. Sprinkle each piece on both sides with salt and pepper. Place 1 cheese slice and 1 ham slice on each breast. Roll up each breast using toothpicks to secure if necessary. Dredge each in flour, shake off excess, then in egg and finally in bread crumbs. Place seam side down in baking dish that has been sprayed with Pam. Place 1 tablespoon butter on each piece of chicken. Bake at 350 degrees fro 35 minutes or until juices run clear (It's been my experience that it can take up to an hour to cook if you don't get the chicken thin enough). Meanwhile, in a saucepan, combine broth and whipping cream; season to taste with salt, pepper, garlic and oregano. Simmer on low, stirring until thickened. Pour over chicken.