Trim the outer crusts from every slice of bread and slice each piece lengthwise into three equal batons. Neat, uniform batons ensure even heat distribution and consistent browning across all sides.
Whisk the eggs, milk, and a pinch of salt together in a wide, shallow bowl until fully blended and streak-free. A completely smooth custard prevents patches of cooked egg white from appearing on the bread.
Stir the ground cinnamon and granulated sugar together across the surface of a wide, flat rimmed plate. Spreading the spiced sugar widely allows you to roll multiple hot batons in a single quick motion.
Heat a large skillet over medium-high heat and melt two tablespoons of the butter until it bubbles and coats the pan. The butter should sizzle vigorously and begin to subside before any bread touches the cooking surface.
Roll the bread sticks swiftly through the egg mixture for roughly two seconds, allow excess liquid to drip off, and place them into the hot skillet in two spaced batches. Moving quickly prevents the interior of the bread from becoming overly saturated and mushy.
Sear the batons for several minutes, turning them onto each of their four sides until every edge turns deep golden brown. The batons should feel firm to the touch with tongs and release a rich, toasted aroma as they cook.
Lift the cooked sticks directly from the hot skillet onto the spiced sugar plate and toss them thoroughly to coat every side. The residual heat and melted butter on the crust melt the sugar crystals slightly, creating an immediate glossy adhere.
Add the remaining tablespoon of butter to the skillet, melt it completely, and cook the second batch of coated sticks. Fresh butter ensures the second round cooks with the same golden crispness and clean flavor as the first.
Transfer the warm cinnamon-coated batons to a serving platter and present them alongside warm maple syrup for dipping. The sugar coating remains crunchiest when enjoyed fresh from the pan.