Before getting started, use a large knife to slice the stale brioche bread into sticks.
Once you're ready to cook your French toast sticks, add the butter to a large skillet over medium-low heat.
In a large mixing bowl, whisk together the milk, egg, light brown sugar, 1 teaspoon of the cinnamon, vanilla and coarse kosher salt. Set aside.
In another large bowl, add the cane sugar and another teaspoon of the cinnamon. Mix together and set aside.
Dip the strips of brioche bread that you sliced up in the first step into the milk mixture, and then transfer to the hot skillet. Let cook for 1 minute in the skillet.
Then flip each bread strip over to cook for an additional minute, or 'til both sides are crisp and golden brown.
Use a pair of tongs to transfer the sticks to the cinnamon sugar mixture, and coat both sides liberally and evenly before moving onto a plate for serving.
That's it! Your French toast sticks are ready to serve immediately with maple syrup and a piping hot cup of coffee!