For a chocolate version, substitute 3/4 pound bittersweet chocolate (either in small chips or chopped from a small block) for the prunes and raisins. Recipe courtesy of Russ and Daughters.
Whisk together eggs, egg yolk, sugar, vanilla, and cinnamon in a large bowl until smooth. Whisk in half-and-half and milk. Add bagel cubes, and toss to coat. Let mixture sit, stirring occasionally, until bread absorbs some of the liquid, about 1 hour.
Preheat oven to 325 degrees. Butter an 8-inch square baking dish (2 inches deep). Stir prunes and raisins into bagel mixture, and transfer to dish. Bake until top is golden brown and a toothpick inserted in center comes out clean, about 1 hour (if top browns too quickly, tent with foil). Let cool completely on a wire rack. Cut into squares, and serve with ice cream.