Cook manicotti according to package directions. For sauce, in a saucepan, saute onion in butter. Stir in flour and salt until blended. Gradually whisk in cream and broth; bring to a boil. Cook and stir for 1-2 minutes or until thick and bubbly. Stir in cheeses just until melted.
In a bowl, combine the eggs, bread crumbs, parsley, pepper flakes, salt and nutmeg. Stir in chicken and broccoli; add 1 cup sauce. Drain manicotti; stuff with chicken mixture.
Spread about 1/2 cup cheese sauce in two greased 11x7-in. baking dishes. Top with manicotti; pour remaining sauce over manicotti. Cover and bake at 350° for 35-40 minutes. Uncover and bake 5 minutes longer or until golden brown.