Beat eggs in medium mixing bowl. Add milk and vanilla, and stir until combined.
In a separate bowl, mix brown sugar and cinnamon sugar. Place a nonstick skillet on the stovetop over medium heat.
Slice individual slices of Brioche bread into thirds, with each slice yielding three sticks.
Melt one tablespoon square of butter in your preheated skillet. You'll cook 18 sticks in five batches, using one tablespoon of butter for each batch. We don't want to crowd the sticks to ensure every edge is adequately caramelized.
Take one stick of butter and coat well in the egg mixture. Move to the sugar bowl, and coat well, ensuring the sugar granules stick to the stick (get it?).
Place three coated sticks into the skillet at a time and cook for about 2 minutes on each side, or 4 minutes total. On our stovetop, 4 minutes was the perfect time, though your own stove may differ so watch closely for that beautiful golden brown color.
Dust with powdered sugar. Serve with maple syrup on the side or if you're feeling decadent (you earned it!), serve with chocolate syrup. A fresh fruit salad never hurts, either.