Step 1: In a medium saucepan, combine water, butter, 1 tablespoon granulated sugar, and salt. Bring this mixture to a rolling boil over medium-high heat, stirring until the butter is fully melted and sugar is dissolved.
Step 2: Once boiling, remove the saucepan from the heat. Add all the all-purpose flour at once. Stir vigorously with a wooden spoon or spatula until a smooth ball of dough forms and pulls away from the sides of the pan.
Step 3: Transfer the hot dough to a large mixing bowl. Let it cool for about 5 minutes.
Step 4: Add the eggs, one at a time, mixing well after each addition. The dough will initially look separated, but continue mixing until it comes together into a smooth, thick, and glossy paste.
Step 5: Fit a piping bag with a large star tip (e.g., Ateco 826 or 827). Spoon the churro dough into the piping bag.
Step 6: In a large, heavy-bottomed pot or Dutch oven, heat 2-3 inches of oil to 350-375°F (175-190°C). Use a candy thermometer to monitor the temperature.
Step 7: Carefully pipe 4-6 inch strips of dough directly into the hot oil, using kitchen shears or a knife to cut the dough from the piping bag. Do not overcrowd the pot; fry in batches to maintain oil temperature.
Step 8: Fry for 2-4 minutes per side, or until golden brown and cooked through. Use a slotted spoon or tongs to carefully flip them.
Step 9: Remove the fried churros from the oil and place them on a wire rack lined with paper towels to drain any excess oil.
Step 10: In a shallow dish, combine 1/2 cup granulated sugar and 1 tablespoon ground cinnamon for the coating. While the churros are still warm, gently toss them in the cinnamon sugar mixture until evenly coated.
Step 11: Serve immediately with your favorite dipping sauce, such as warm chocolate sauce or dulce de leche.