This homey dessert is a cross between bread pudding and French toast. To create an elegant presentation, cut the Pain Perdu neat rounds with a biscuit cutter or a drinking glass.
Preheat oven to 350 degrees. Trim side and bottom crusts from brioche, leaving top crust intact. Slice brioche 1/4 to 1/3 inch thick. Butter a 9-by-13-inch baking pan; lay bread pieces in pan so that they overlap slightly, with top crusts visible.
Make custard: In a medium saucepan over medium heat, whisk milk, cream, sugar, vanilla scrapings, and liqueur. Cook until hot but not simmering.
In a large bowl, whisk together eggs and yolks. Whisking constantly, pour 1 cup of the hot milk mixture into eggs; slowly add remaining milk mixture.
Pour custard over bread, making sure to soak completely. Bake until firm to the touch, about 1 hour; if needed, press bread with a spatula to keep it moist.
Remove from oven. Let cool slightly before cutting into rounds with a 3-inch biscuit cutter. Serve warm.