01 - Preheat the oven to 350°F. Thoroughly grease a 9x13-inch baking dish with butter to prevent sticking.
02 - Scatter the cubed cinnamon rolls evenly over the base of the prepared baking dish.
03 - In a large mixing bowl, briskly whisk together eggs, whole milk, heavy cream, granulated sugar, brown sugar, vanilla extract, ground cinnamon, and salt until the mixture is fully combined and smooth.
04 - Evenly pour the custard over the cinnamon roll cubes. Gently press the bread cubes into the liquid to ensure each piece is saturated.
05 - Allow the mixture to stand at room temperature for 10 minutes so the cinnamon rolls soak up the custard.
06 - Transfer the dish to the oven and bake for 40 to 45 minutes, or until the pudding is set and a knife inserted into the center emerges mostly clean with only a few moist crumbs.
07 - While the pudding bakes, combine whole milk, heavy cream, granulated sugar, and unsalted butter in a medium saucepan over medium heat. Stir continuously until the sugar has dissolved and the mixture is hot but not boiling.
08 - Whisk cornstarch and cold water together in a small bowl until smooth and fully incorporated.
09 - Gradually whisk the cornstarch slurry into the hot saucepan mixture. Continue stirring until the sauce thickens, about 2 to 3 minutes.
10 - Remove the saucepan from heat and stir in the vanilla extract and a pinch of salt. Blend thoroughly.
11 - Allow the bread pudding to cool briefly. Serve warm portions generously drizzled with vanilla sauce.