Prepare the churro cinnamon sugar. In a shallow bowl combine the sugar, brown sugar, and cinnamon until everything is incorporated. Set aside.
½ cup granulated sugar, ¼ cup brown sugar, 3 teaspoons ground cinnamon
In a medium bowl whisk together the eggs, milk, brown sugar, cinnamon, and vanilla until everything is well combined.
3 large eggs, 2 cups milk, 3 tablespoons brown sugar, 1 teaspoon ground cinnamon, ½ teaspoon pure vanilla extract
Set a large frying pan or cast iron skillet over medium heat. Add 1 tablespoon of butter to the pan and let it melt.
4 tablespoons unsalted butter
Dredge 2 slices of bread at a time through the egg mixture, then cook, flipping once, until browned and cooked through.
8 slices brioche bread
Immediately dip the hot toast in the cinnamon-sugar mixture, flipping to coat. Place on a wire rack.
Repeat with the remaining slices of bread, adding 1 tablespoon of butter to the pan between slices.
Serve immediately or place in a 250°F oven on a wire rack set in a rimmed baking sheet until ready to serve.