Heat oven to 350 F. Butter a 13 x 9 x 2-inch baking dish.
Bring a large pot of water to a boil. Add onions and cook for 10 minutes. Drain and spoon into prepared baking dish.
Meanwhile, melt butter in a medium-size saucepan. Whisk in flour, salt and pepper until smooth. Gradually whisk in the milk and bring to a boil. Boil for 1 minute, whisking constantly. Stir in cheese over low heat until cheese is melted.
Pour sauce over onions and stir to combine completely. Arrange bread cubes over mixture.
Bake at 350 F for 27 to 30 minutes or until bread is golden and onions are bubbling. Allow to stand for 10 minutes before serving. Garnish with chives, if desired. Do-Ahead Tip: If not serving right away, allow to cool completely. Cover and refrigerate for up to 2 days. To serve, bring to room temperature. Gently reheat at 325 F for 30 minutes or until internal temperature registers 150 F on an instant-read thermometer.