Grease casserole dish with butter or non stick cooking spray. Set aside.
In a mixing bowl, whisk together half & half, eggs, salt and pepper. Set aside.
Slice a loaf of French bread into 1½ inch thick slices.
Spread Dijon mustard onto each of the slices of French bread.
Place half the slices of bread in the prepared baking dish, mustard side facing up.
Spoon half the egg mixture over the slices of bread.
Add a layer of half the sliced green onions, all of the diced ham, and half the grated Gruyère and Mozzarella cheeses.
Top with remaining slices of French bread, mustard side facing down.
Spoon remaining egg mixture over the slices of bread, making sure to saturate each slice of bread.
Top with the remaining grated Gruyère and Mozzarella cheeses.
Cover the casserole dish with foil and refrigerate overnight.
Preheat oven to 350℉.
Remove casserole dish from the fridge and allow it to come to room temperature while oven preheats.
Bake covered for 40 minutes.
Remove foil and top with remaining green onions.
Bake casserole for another 15-20 minutes or until cheese is hot and bubbly and light golden brown.
Remove from oven and allow casserole to rest for 10 minutes before slicing into it.