Preheat the oven to 350°F (180°C).
Grease a 9x13-inch (23x33cm) oval baking dish with butter.
Cut the brioche into roughly 1-inch (3cm) cubes and place them in the baking dish
In a large bowl, whisk together all the remaining ingredients: eggs, milk, sugar, cinnamon, vanilla, and salt. (You can also use an electric mixer.)
Pour the custard over the brioche cubes in the baking dish. Gently move the cubes around to ensure they are evenly coated with the custard (egg-milk mixture) on all sides. Press the cubes slightly to help them absorb the custard. The mixture should almost cover the brioche cubes, with the tips sticking out slightly to crisp up during baking.
Bake for about 40 minutes, or until the top is golden and crispy and the custard is set. (To check for doneness, the center should not jiggle, and the internal temperature should reach 160°F/71°C.)
Enjoy!