To make the French toast sticks: Preheat the oven to 350°F (180°C). Line a large baking sheet with parchment paper, spray the parchment paper lightly with nonstick cooking spray, and set aside.
Slice each piece of Texas toast lengthwise into 3 pieces. Set aside.
In a shallow baking dish, whisk the lightly beaten eggs, whole milk, heavy cream, and vanilla extract together until fully combined.
In a small mixing bowl, whisk together the 1 tablespoon of granulated sugar and ½ teaspoon ground cinnamon. Add the cinnamon sugar mixture to the egg mixture and whisk until fully combined.
Quickly dip each piece of bread into the egg mixture, making sure to fully coat it. Allow any excess to drip off and place onto the prepared baking sheet, leaving a little room between each one.
Bake for 10 minutes, remove from the oven, and use tongs to flip each one. Return to the oven and bake for an additional 6 to 10 minutes or until the french toast sticks are firm and fully cooked through. Remove from the oven.
To make the cinnamon sugar coating: Lightly brush the top of each stick with the melted butter (I use a pastry brush for this step). Using tongs, flip each one, and lightly brush the other side of each stick with more butter.
Whisk the granulated sugar and ground cinnamon together until well combined and transfer the mixture to a large plate.
Add the french toast sticks to the cinnamon sugar mixture and toss to coat each one. If you have any additional cinnamon sugar leftover, you can dip the sticks in it again, or sprinkle it on top right before serving.