In a medium saucepan, combine water, butter, 2 tablespoons sugar, and salt. Bring to a boil over medium-high heat.

Remove saucepan from heat and stir in the flour with a wooden spoon until a smooth ball of dough forms.

Allow the dough to cool for 5 minutes, then beat in the egg and vanilla extract until the mixture is glossy and smooth.

Heat vegetable oil in a deep heavy-bottomed pot or Dutch oven to 375°F (190°C).

Transfer the dough to a pastry bag fitted with a large closed-star tip.

Pipe 4-inch lengths of dough into the hot oil, cutting the ends with kitchen shears.

Fry 3 to 4 churros at a time for 2 to 3 minutes per side until evenly golden-brown.

Remove churros with a slotted spoon and drain briefly on paper towels.

In a shallow bowl, whisk together the coating sugar and cinnamon.

While still warm, toss the fried churros in the cinnamon-sugar mixture until fully coated.