1In small skillet, cook mushrooms in butter for 5 minutes. Blend in the 2 Tbspl. of flour. Stir in the cream. Add salt and cayenne pepper. Cook, stirring til the mixture is very thick. Add cheese and simmer, stirring til cheese melts. Turn mixture into a pie plate. Cover and chill for 1 hour. Cut into 6 pieces, shaping into short sticks.
2Remove skin from chicken breasts. Place each piece of chicken between plastic wrap and pound out with a wooden mallet to form cutlets not quite 1/4 inch thick. Peel off the wrap. Sprinkle the chicken with more salt.
3Put a cheese stick on each piece, tucking in the sides. Roll as you would if you were making a jelly roll. Press to seal well. Dust the rolls with flour. Dip rolls into the egg, then in the bread crumbs. Cover and chill thoroughly for at least 1 hour.
An hour before serving, preheat oven to 350. Fry rolls in a little oil to brown. Transfer to a baking dish and bake for 30 to 45 minutes.