Heat the oven to 350°F and butter a 9-by-13-inch dish. Spread the bagel pieces in the dish with the salmon, cream cheese and capers.
Whisk the eggs, milk, pepper and dill until combined, then pour evenly over the bagels.
Press the bread down, cover and soak for 30 minutes in the refrigerator, additional to the listed active prep time.
Bake covered with foil for 25 minutes. Uncover and bake for 15 to 20 minutes more, until the center reaches 160°F and no milky custard remains between the pieces.
Rest for 10 minutes before serving; cut through the chewy bagel edges with a serrated knife.