Layer cubed bread, ham, and cheese evenly into 2 greased 8-oz. ramekins or individual soufflé dishes.
Whisk together eggs and next 5 ingredients. Pour evenly over cheese in ramekins. Cover and chill 8 hours. Let stand at room temperature 20 minutes before baking.
Bake at 350° for 20 to 25 minutes or until set. Let stand 5 minutes before serving.
Note: To bake in a muffin pan, layer cubed bread, ham, and shredded cheese evenly in 4 greased cups in pan. Pour egg mixture evenly over cheese in muffin cups. Cover and chill 8 hours. Let stand at room temperature 20 minutes before baking. Bake at 350° for 15 to 20 minutes or until set. Let stand 5 minutes before serving.