Toast the bagels and cut them up into cubes. Place them into a 9x13 baking dish.
Using a handheld electric mixer, beat the eggs, cream cheese and milk or half-and-half together. Stir in the smoked salmon, capers and chives. Pour the mixture over the bagels. Cover with plastic wrap and weigh down with another baking dish. Refrigerate overnight or at least 1 hour.
When ready to bake, preheat oven to 350 degrees. Unwrap the casserole and top with slices of Swiss cheese. Bake 45 minutes.