Preheat your oven to 400° Fahrenheit. Line a baking sheet with parchment paper.
Combine the butter, milk, water, brown sugar, and one tablespoon of white sugar in a medium or large saucepan. Cook the ingredients over medium heat until the butter is fully melted.
Reduce the heat to low and whisk in the flour until it is fully incorporated into the melted butter mixture.
Turn off the heat and whisk in the eggs one at a time. Ensure that each egg is fully incorporated into the churro batter before adding a new one.
Transfer your batter to a piping bag equipped with a star-tip nozzle.
Slowly pipe logs about 6 inches long onto your baking sheet.
Bake your churros for 20 minutes, and then turn off the oven. Allow your churros to cool inside the oven for 10 minutes.
Place your churros in a gallon-sized Ziploc bag with the cinnamon and remaining granulated sugar. Shake the bag a few times to evenly coat the churros.