Melt the butter or margarine in a good-sized saucepan. Stir in the flour. Skim the fat from the surface of the broth and add the broth alternately with the cream, stirring constantly. Bring to a boil. If the sauce is thicker than heavy cream, add a little more of each liquid. Beat the egg thoroughly. Add a small quantity of the gravy to the egg, then pour back into kettle. Add the chicken, carrots, peas, onions, and chopped parsley. Taste; add salt and pepper if needed.

Pour the mixture into a 2-quart casserole and place in a 425 degrees F oven. Heat until it bubbles vigorously. As quickly as possible, arrange unbaked biscuits on top of the pie and return to the oven for 10 to 15 minutes or until the biscuits are done.