Slice the brioche bread into slices that are ½ to ¾ inch thick.
In a shallow bowl or baking dish, whisk together the eggs, vanilla, and maple syrup until smooth and homogenous. Whisk the milk into the egg mixture.
Depending on the size of your bowl and pan [I find a square baking dish works very well for this task], place 1-3 pieces of bread in the batter. Let it absorb for 5 minutes and then flip.
Preheat a skillet, griddle, or cast-iron pan over medium-low heat. Add about 2 teaspoons of butter and swirl to coat.
When the pan is warm but not smoking hot, transfer the soaked bread from the bowl to the pan, allowing the excess to drip off before cooking.
While the first batch cooks, begin soaking the next batch. Cook for 5 minutes or until golden brown, and flip each slice of French toast.
Continue cooking on the second side until the centers feel set when lightly touched with your finger and both sides are a golden brown. Add more butter to the pan if needed. Think of this like cooking bread pudding or this breakfast casserole with bread.
Move the French toast to a wire rack set on a baking sheet. Keep warm in a warm oven until ready to serve, or serve immediately! Continue with the remaining slices of bread.