Lightly grease a small baking dish, such as a 8x8" pan, or a small casserole dish. Layer half of the bread cubes on the bottom. Layer the cheese cubes and the ham over the bread. (Note: At this point, you can layer some chopped spinach over the ham/cheese, if desired ... but make SURE the spinach is well-drained, and squeezed VERY dry!
Top with the remaining bread cubes. Dot with butter.)
In a small bowl, beat together the eggs, milk, seasonings, and onion flakes.
Pour the milk mixture over the entire bread mixture. Sprinkle shredded cheese on top. Sprinkle with paprika.
Refrigerate overnight, or at least a couple of hours.
Preheat oven to 375°. Bake for 45 minutes, until set. Serve hot, with a salad, if making for dinner. If you're using this for a brunch, some fresh fruit on the side is nice, like pineapple or a fresh fruit salad.
Note: if you really like cheese, add extra. I do, and nothing's better than a "little extra cheese". :o)