1. Grease a shallow 1½-quart baking dish. In a large bowl, whisk the three milks, eggs, cinnamon, and vanilla until well blended.
2. Arrange the bread in an even layer in the dish. Pour the milk mixture over the bread. Cover with plastic wrap and refrigerate for at least 1 hour and preferably overnight.
3. Preheat the oven to 350°F. Uncover the dish and bake until puffed and golden brown and a knife inserted in the center comes out clean, about 1 hour. Let stand 10 minutes before cutting. Sprinkle with cinnamon if desired.