In a medium saucepan, combine water, butter, 2 tablespoons of sugar, and salt. Bring the mixture to a rolling boil over medium-high heat, then remove it from the heat.

Add the all-purpose flour to the hot liquid and stir vigorously with a wooden spoon until a smooth ball of dough forms. Continue stirring for about 1 minute to cook the flour, then allow it to cool for 5 minutes.

Beat the eggs into the cooled dough one at a time, ensuring each egg is fully incorporated before adding the next, until the dough is smooth and glossy.

Heat vegetable oil in a deep heavy-bottomed pot or Dutch oven to 375°F (190°C), maintaining a depth of at least 2 inches of oil.

Carefully pipe the churro dough into the hot oil, using a star-tipped piping bag; fry in batches until golden brown and crispy, about 2-3 minutes per side. Carefully remove the cooked churros with tongs or a slotted spoon and place them on a paper towel-lined plate to drain.

Mix the remaining 1/2 cup sugar and ground cinnamon in a shallow dish, then roll the warm churros in the cinnamon sugar mixture until evenly coated before serving.