Preheat oven to 375 degrees F (190 degrees C). Grease a 9-inch square casserole dish.
Place a steamer insert into a saucepan and fill with water to just below the bottom of the steamer. Bring water to a boil. Add broccoli, cover, and steam until tender, 2 to 4 minutes.
Mix steamed broccoli, bread cubes, diced tomatoes, ham, and pepper jack cheese together in a large bowl.
Beat eggs, cream, garlic powder, salt, and pepper together in a separate bowl; stir into broccoli mixture. Pour mixture into the prepared casserole dish.
Bake in the preheated oven until eggs are set in the middle, about 35 minutes. Allow to cool for 3 to 5 minutes before cutting.
