Grease a 9×13-inch baking dish and spread the cubed brioche or challah evenly inside.
In a bowl, mix the softened cream cheese, powdered sugar, and vanilla until smooth. Drop small dollops all over the bread cubes, tucking a few down between pieces.
In a large bowl, whisk together the eggs, milk, cream, granulated sugar, brown sugar, vanilla, cinnamon, nutmeg, and salt.
Pour the custard evenly over the bread and cream cheese dollops. Lightly press the bread so everything absorbs the mixture. Cover and refrigerate overnight (or at least 6 hours).
In a medium bowl, combine the softened butter, brown sugar, flour, cinnamon, and salt. Mix with a fork or your hands until crumbly.
Preheat the oven to 350°F. Sprinkle the streusel evenly over the chilled casserole. Bake uncovered for 40–50 minutes, until the top is golden and the center is set but still slightly soft.
Let it cool for 10 minutes so the custard sets. Serve warm with powdered sugar, maple syrup, or fresh berries.