In a food processor, combine butter and sugar briefly, just until it forms into a ball. Add eggs, heavy cream, cinnamon, and vanilla, and process until blended.
Lightly butter a 9 by 13-inch baking dish. Break up the doughnuts into 1-inch pieces and layer in the pan. Scatter the raisins over the top. Pour the egg mixture over the doughnuts; soak for 5 to 10 minutes. You will need to push doughnut pieces down during this time to ensure even coverage by egg mixture.
Cover with foil and bake for 35 to 40 minutes. Remove foil and bake for additional 10 minutes to brown the top. The doughnut bread pudding is done when the custard is set, but still soft.
Make the rum sauce: melt butter over medium heat in a saucepan, and take off the heat. Add confectioners' sugar to the melted butter and whisk to blend. Add rum, to taste. Pour the sauce over the bread pudding and allow to soak in.