Grease a 2-quart baking dish. Place the cubed cake in the prepared pan.
Whisk together the eggs, milk, sugar, cookie butter, vanilla, and cinnamon. Pour over the cake in the pan, pressing the cake down into the mixture if needed.
Refrigerate the mixture for an hour to overnight.
Remove the chilled bread pudding from the refrigerator to sit at room temperature while the oven heats. Preheat oven to 350°F (175°C).
Bake for 1 hour to 1 hour 10 minutes, or until a knife inserted into the center comes out clean.
Serve warm with warm vanilla sauce.
To make the sauce:
Place the butter, sugar, brown sugar, cream, and salt in a heavy saucepan***. Cook over medium heat until bubbly and thickened (about 4-6 minutes).
Remove the pan from the heat. Carefully stir in the vanilla.
Spoon over servings of warm bread pudding.
Notes
*Homemade or store-bought. My favorite is Cream Cheese Pound Cake (a half recipe). If your cake isn't a few days old, then toast it at 350°F for 7 to 10 minutes.
**Look for cookie butter alongside other spreads, like peanut butter.
**The mixture will be quite bubbly while it cooks, so be sure to use a large enough pan.