Grease a 2.5-quart baking dish and place bread cubes evenly inside.
In a large bowl, whisk eggs, milk, half and half, brown sugar, cinnamon, and vanilla until well combined.
Pour custard mixture evenly over the bread. Press down gently to help bread absorb the liquid. Cover and refrigerate overnight.
For the topping: combine brown sugar, flour, cinnamon, and salt. Add butter and mix with fingers or a fork until crumbly. Cover and chill.
When ready to bake, preheat oven to 350°F (175°C). Crumble topping evenly over the casserole.
Bake uncovered for 40–55 minutes, or until golden, puffed, and set in the center.
Let cool slightly. Serve warm with maple syrup.