Butter a 9-by-13-inch baking dish.
For the casserole: Trim the ends from 1 loaf day-old brioche (about 1 pound) and cut into ten 1-inch thick slices. Cut each slice in half diagonally to make two triangles from each piece. (If the bread is fresh, dry it out a bit. Place the slices in a single layer on a baking sheet and bake at 300 degrees F for 10 minutes, flipping halfway through.)

Whisk together the eggs, cream, milk, brown sugar, vanilla, cinnamon, nutmeg and 1/4 teaspoon salt in a large bowl until well blended. Dip each triangle of bread in the custard, lightly coating each side. Shingle the pieces in the prepared pan, overlapping slightly.

Pour any remaining custard over the bread slices. Cover the dish with plastic wrap and place in the refrigerator for at least 6 hours or up to overnight.

When ready to bake, preheat the oven to 350 degrees F. Remove the casserole from the refrigerator and let rest 15 to 20 minutes at room temperature before baking. Remove the plastic wrap and bake until the casserole is golden and puffed and the custard is set, 45 to 50 minutes.