Make a cream sauce if the butter, flour, milk, and salt. Stir until is is smooth and thick. Add a little to the egg yolks and blend back into the cream sauce. Cook a minute or two more, do not let sauce boil. Stir in tabasco sauce and cheese.
Arrange broccoli on bottom of 9x13 dish, add a thin layer of cream sauce, arrange chicken pieces on broccoli. Cover with rest of cream sauce. Sprinkle with crackers.