Place a rack in the upper third of the oven; preheat to 300 degrees . Spread the bagel pieces on a rimmed baking sheet. Bake, stirring once, until toasted, about 30 minutes; let cool. Increase the oven temperature to 375 degrees .
In a large skillet, cook the bacon over medium heat, stirring often, until crisp, about 7 minutes. Transfer to a paper towel-lined plate. Add the onion to the bacon drippings and cook, stirring occasionally, until soft, about 5 minutes.
In a large bowl, whisk together the broth and the eggs; season. Add the bagel pieces, bacon, onion and parsley; toss to combine. Let stand, tossing occasionally, for 15 minutes. Transfer to a greased shallow 2 1/2-qt. baking dish. Bake until the top is browned, about 45 minutes.