Heat oven to 350°F. Butter 13x9-inch (3-quart) glass baking dish. In baking dish, place half of bread cubes. Top with banana slices and remaining bread cubes. In large bowl, blend eggnog, eggs, granulated sugar and nutmeg. Pour over bread cubes. Let stand 5 minutes.
Bake 40 to 50 minutes or until knife inserted in center comes out clean.
Meanwhile, in small saucepan, cook all sauce ingredients except rum extract over medium heat, stirring constantly, until mixture boils and thickens. Reduce heat to low; simmer 5 minutes, stirring constantly. Stir in rum extract. Serve warm sauce over pudding.