Cook chicken breasts in boiling salted water until tender. Drain, reserving 2 cups broth. Let chicken breast cool to touch; discard skin. Thinly slice chicken breasts to yield 18 slices; set aside.

Cook broccoli in a small amount of boiling salted water just until crisp-tender; drain well, and set aside.

Melt butter in a heavy saucepan over low heat; add flour, stirring until smooth. Cook 1 minute, stirring constantly. Gradually stir in reserved broth, whipping cream, and sherry; cook over medium heat, stirring constantly until thickened and bubbly. Stir in salt and pepper; remove from heat.

Arrange broccoli in a lightly greased 13x9x2" glass baking dish; top with half of sauce. Arrange chicken slices over broccoli. Stir 1/4 cup parmesan cheese into the remaining sauce; spoon over chicken. Sprinkle with 2 tablespoons Parmesan cheese.

Bake at 350 degrees for 20 to 25 minutes or until bubbly; then broil 2 minutes or until top of casserole is delicately browned.