Grease a 13x9 inch casserole dish.
Cut bread into small cubes and place them in the prepared casserole dish in an even layer along the bottom.
Top with 2 cups shredded cheese, reserving some for another layer.
Top with all the diced ham.
In a large bowl whisk together eggs, milk, salt and dry mustard.
Grate just the broccoli florets using the finest shred on a box grater.
Stir in grated broccoli to combine.
Pour the egg mixture over the bread cubes, cheese and ham in the casserole dish.
Top with remaining ½ cup of shredded cheese.
Cover casserole dish with foil and place in the refrigerator overnight.
In the morning remove casserole from the fridge and allow it to sit on the counter while oven preheats to 375℉.
Bake covered for 30 minutes.
Remove foil and bake for another 20-30 minutes until center is set and heated through and cheese is hot and bubbly.
Turn oven temperature to broil and cook until lightly toasted.