Preheat oven to 325 degrees F. Grease a 2-quart rectangular baking dish. Spread half of the bread cubes in the dish. If desired, snip some of the green feathery tops from the fennel bulb and reserve for a garnish. Trim, core, and chop fennel bulb to make 1 cup. Sprinkle fennel evenly over bread in dish. Top with ham, apple, cheese, and 1/2 cup green onions. Top with remaining bread.