Preheat the oven to 350°F (175°C). Line an 18x13-inch baking sheet with parchment paper.

In a small bowl, whisk together 2 tablespoons granulated sugar and 1 teaspoon ground cinnamon; set the cinnamon-sugar mixture aside.

In a medium bowl, vigorously whisk 1 cup whole milk, 4 large eggs, 1 teaspoon vanilla extract, and 1 pinch salt until very well blended.

Cut each of the 8 slices of Texas toast into three even strips. You may layer slices to cut several at a time.

Working a few sticks at a time, dip each bread strip into the egg mixture, turning to coat both sides. Lift each strip and let excess drip back into the bowl.

Arrange the coated sticks on the prepared baking sheet in a single layer, fitting them closely but leaving a little space between each stick.

Using a basting brush, brush the tops of the french toast sticks lightly with 1 tablespoon of the melted butter.

Evenly sprinkle half of the reserved cinnamon-sugar mixture over the brushed tops.

Bake in the preheated oven for 13 minutes.

Remove the baking sheet from the oven, flip each french toast stick to the opposite side, and brush the now-top sides lightly with the remaining 1 tablespoon melted butter.

Evenly sprinkle the remaining half of the cinnamon-sugar mixture over the sticks, return the pan to the oven, and continue baking until cooked through and lightly golden, about 13–18 minutes longer.

Let the french toast sticks cool on the baking sheet for a few minutes. Brush lightly with a little more melted butter if desired, and serve warm with maple syrup for dipping.