In a large bowl, whisk together: eggs, whole milk, half and half, maple syrup, vanilla, cinnamon, and salt.
One slice at a time, place the sourdough bread slices into the egg mixture and turn several times to coat well. Place the bread slices in a 9x13 baking dish. If you're using a boule, you should have 3 slices on the bottom, followed by 2 more layers (you'll have 2 slices on top). Pour the remaining egg mixture, evenly, on top. Cover with plastic wrap, and refrigerate overnight.
In the morning, preheat the oven to 400 degrees F. and generously grease a light-colored non-stick sheet pan with butter (preferred) or cooking oil spray.
Set the top layer of bread slices aside and place the bottom layer pieces onto the sheet pan, allowing any excess egg mixture to drip back into the dish. Place the top slices back into the baking dish to soak up any remaining egg mixture and place them onto the sheet pan.
Bake for 8 minutes, flip and brush with melted butter, and bake 6-8 minutes more until puffed and lightly golden.
While warm, brush with melted butter (if desired), and garnish with your favorite toppings. Enjoy immediately for the best texture.