Make the Bread Pudding Base: Spray an 8-inch baking dish with nonstick cooking spray. Separate the cinnamon rolls and cut each into quarters. Scatter into the pan. In a medium bowl, stir the butter, brown sugar, and cinnamon together until combined. Add the eggs, one at a time, beating well after each is added. Stir in the milk and vanilla, then pour mixture evenly over the bread. Refrigerate at least 6 hours, or overnight. Preheat the oven to 350ºF. While oven is preheating, make the streusel. Use a fork to cut the butter into the brown sugar, flour, and cinnamon until mixture resembles coarse crumbs. Sprinkle streusel evenly over the dish. Cover bread pudding with foil, and bake for 40-45 minutes. Remove foil during last 15 minutes of baking.
Make the Cream Cheese Icing: In the bowl of a stand mixer fitted with the paddle attachment, beat the butter and cream cheese together until smooth. Add the powdered sugar, vanilla, and lemon juice and continue beating until combined. Spread evenly on top of the warm bread pudding. Serve and enjoy!