Step 1: Prepare the Cinnamon Sugar - In a small bowl, combine 1/2 cup of sugar with 1/2 teaspoon of ground cinnamon. Set this mixture aside for coating the churros.
Step 2: Make the Dough - In a medium saucepan, melt 4 ounces of butter over medium heat. Add 1 cup of water, 2 tablespoons of white granulated sugar, 1 teaspoon of pure vanilla extract, 3/4 teaspoon of ground cinnamon, and 1/2 teaspoon of salt. Stir until boiling.
Step 3: Add Flour - Remove from heat and quickly stir in 1 1/4 cups of all-purpose flour. Mix until a dough forms and pulls away from the sides.
Step 4: Incorporate Eggs - Allow the dough to cool for about 5 minutes. Add 2 eggs, one at a time, mixing well after each addition until smooth.
Step 5: Heat Oil - In a deep frying pan or pot, heat oil to 350°F (175°C) enough to submerge the churros.
Step 6: Pipe the Churros - Transfer the dough to a piping bag with a star tip. Pipe strips into the hot oil, cutting to desired length.
Step 7: Fry Until Golden - Fry churros for about 2-3 minutes on each side until golden brown. Remove with a slotted spoon and drain on paper towels.
Step 8: Coat with Cinnamon Sugar - Roll warm churros in the cinnamon sugar mixture until fully coated. Serve immediately with dipping sauces!