Add the cooked and drained broccoli to a 7x11 baking dish.
Cut eggs in half lengthwise, remove yolks to a bowl.
Mash yolks and mix with the mayo, onion, mustard, and Worcestershire sauce, taste and season with salt and pepper as desired. Mix in ½ of the deviled ham.
Place a small amount of deviled ham in each egg white.
Divide yolk mixture among all the whites, and top each with another small amount of the remaining deviled ham.
Arrange deviled eggs on the broccoli.
Preheat your oven to 180° C (350° F).
In a sauce pan, melt the butter, stir in the flour. Slowly add milk while stirring. Stir continuously until thickened.
Stir in cheese and salt, stir until cheese is melted in and smooth.
Pour sauce over eggs to cover them.
Bake for 20-25.
Serve and enjoy.