Preheat the oven to 350 degrees F. Grease a 9x13 baking dish or 12-inch round cast iron skillet with cooking spray. Cut the brioche bread into one inch cubes and set aside.
In a large bowl, combine milk, heavy cream, melted butter, bourbon, eggs, cinnamon, nutmeg, and vanilla extract. Whisk together until combined.
Mix together the cinnamon streusel. Add cinnamon, brown sugar, flour, and a pinch of kosher salt to a small bowl. Whisk together and then pour in melted butter and mix until the texture resembles wet sand.
Add the bread cubes to the prepared pan and pour the custard on top, mixing around to ensure that all of the bread is coated. Then add the streusel on top. Bake for 40-45 minutes, until the bread looks puffy and golden brown.
While the bread pudding is baking, prepare the vanilla sauce. Add heavy cream, milk, sugar, and butter to a small saucepan over medium low heat. Once the butter has melted, warm for 5 minutes (do not boil). Combine cornstarch and 2 tbsp of half and half or milk in a small bowl to create a slurry. Add to the pan and whisk everything together. Whisking constantly, allow the sauce to thicken, about 5-7 minutes. Remove from heat and add vanilla bean paste and kosher salt.
Combine cornstarch and 2 tbsp of half and half or milk in a small bowl to create a slurry. Add to the pan and whisk everything together. Whisking constantly, allow the sauce to thicken, about 5-7 minutes. Remove from heat and add vanilla bean paste and kosher salt.
Pour the vanilla sauce over the bread pudding.
Notes
Don't Overbake: Bake until the center is just set and the edges are golden. Overbaking dries out the pudding. You can also stick a knife in the center of the bread pudding - if it comes out clean or with just a few crumbs, it's done!
Choose the Right Bread: Use day-old or stale brioche or challah. Stale bread absorbs the custard better without becoming mushy. I've never used sliced/loaf white bread so I would stick to brioche or challah.
Cut Bread Evenly: Cube the bread into uniform sizes to ensure even soaking and baking.
Let It Rest: Allow the pudding to cool slightly before serving to let the custard set.