In a medium saucepan, combine the water, 2 tablespoons sugar, salt, and butter. Bring to a rolling boil over medium-high heat, stirring occasionally until the butter melts completely.

Remove the pan from heat and immediately add all the flour at once. Stir vigorously with a wooden spoon until the mixture forms a smooth ball and pulls away from the sides of the pan, about 1 minute.

Return the pan to medium-low heat and cook the dough for 2 minutes, stirring constantly, to dry it out slightly. You'll see a thin film form on the bottom of the pan.

Transfer the dough to a large bowl and let it cool for 5 minutes. Beat in the eggs one at a time, mixing thoroughly after each addition until the dough is smooth, glossy, and holds its shape when piped.

Heat 2 inches of vegetable oil in a large, heavy-bottomed pot to 375°F. While the oil heats, combine the 1/2 cup sugar and cinnamon in a shallow dish and set aside.

Transfer the dough to a piping bag fitted with a large star tip. Pipe 4-inch lengths of dough directly over the hot oil, using scissors to cut each churro and let it drop into the oil. Fry 4-5 churros at a time to avoid overcrowding.

Fry for 2 minutes on the first side until deep golden brown, then flip and fry for another 1-2 minutes until evenly browned and crispy all over.

Remove the churros with a slotted spoon and drain briefly on paper towels. Immediately toss the hot churros in the cinnamon-sugar mixture until fully coated.

Serve warm within 30 minutes for the best texture. Repeat the piping and frying process with the remaining dough, maintaining the oil temperature between batches.