Preheat oven to 250 degrees F. Line 2 baking sheets with parchment paper. Spread the doughnut pieces on baking sheets and bake about 30 minutes until dry on the outside and semi-firm in the center. Raise the oven temp to 350 degrees F.
In a large bowl, whisk 2 cups of cream with milk, egg yolks, whole eggs, and condensed milk. Add doughnut pieces and let soak until the pieces are softened, about 1 hour, stirring every 15 minutes.
Lightly butter a 9x13 baking dish. Spoon the doughnut mixture into prepared baking dish and cover with foil. Set the dish in a roasting pan and add enough water to reach halfway up the side of the baking dish. Bake the bread pudding for about 40 minutes. Remove foil and bake for about 20 minutes longer or until pudding is set.
Preheat broiler. Broil the pudding for about 3 minutes or until top is lightly browned. Let cool 30 minutes.
In medium bowl, whip the remaining 2 cups heavy cream to semi-soft peaks. Stir in espresso. Serve with warm bread pudding.