Step 1: In a medium saucepan, combine the water, butter, and salt. Bring to a rolling boil over medium-high heat, stirring until the butter is melted.
Step 2: Remove the saucepan from the heat. Add the flour all at once and stir vigorously with a wooden spoon until a smooth ball of dough forms and pulls away from the sides of the pan.
Step 3: Return the saucepan to low heat and cook the dough for 1-2 minutes, stirring constantly, to dry it out. Remove from heat.
Step 4: Transfer the hot dough to a large mixing bowl. Beat in the eggs one at a time, incorporating each egg completely before adding the next. Stir in the vanilla extract until the dough is smooth and glossy.
Step 5: Heat the vegetable oil in a large, heavy-bottomed pot or Dutch oven over medium-high heat to 375°F (190°C). Use a candy thermometer to monitor the temperature.
Step 6: While the oil heats, combine the granulated sugar and cinnamon in a shallow dish. Set aside.
Step 7: Transfer the dough to a piping bag fitted with a large star tip (such as an Ateco 826 or 828).
Step 8: Carefully pipe 4-6 inch strips of dough directly into the hot oil, cutting the dough with kitchen shears. Do not overcrowd the pot; fry in batches.
Step 9: Fry for 2-3 minutes per side, or until golden brown and cooked through. Use tongs to turn the churros as needed.
Step 10: Remove the fried churros with a slotted spoon and place them on a paper towel-lined plate to drain excess oil. Immediately roll the hot churros in the cinnamon sugar mixture until fully coated.
Step 11: Serve warm with your favorite dipping sauce, such as chocolate or caramel.