Make the cinnamon sugar: In a shallow dish, mix 1/2 cup sugar with 1–2 teaspoons cinnamon. Set aside for coating while the churros are warm.

Heat the oil: Pour vegetable oil into a heavy pot to about 2 inches deep. Heat over medium to medium-high until it reaches 350–365°F (175–185°C). Keep a thermometer clipped to the side if you have one.

Start the dough: In a medium saucepan, combine water, butter, 1 tablespoon sugar, and salt. Bring to a gentle boil, then reduce heat to low.

Add the flour: Dump in the flour all at once. Stir vigorously with a wooden spoon until a smooth dough forms and pulls away from the sides, about 1–2 minutes. You’ll see a thin film on the pan—that’s good.

Cool slightly: Transfer the dough to a bowl and let it cool for 3–5 minutes. It should be warm, not hot, so the eggs don’t scramble.

Beat in eggs and vanilla: Add vanilla and one egg. Mix until fully absorbed—it will look gloppy at first, then smooth. Add the second egg and beat again until glossy and pipeable.

Prep the piping bag: Fit a piping bag with a large open star tip (like 1M or 829). Spoon in the dough. If you don’t have a piping bag, use a heavy zip-top bag with a corner snipped (the ridges won’t be as defined, but it works).

Test the oil: Pipe a 1-inch strip of dough and carefully drop it in. If it sizzles steadily and turns golden in about 2 minutes per side, you’re good to go.

Pipe and fry: Pipe 4–6-inch lengths directly into the oil, cutting the dough with scissors or a knife. Fry in batches to avoid crowding. Cook for 2–3 minutes per side until deep golden brown.

Drain and coat: Remove with a slotted spoon to a paper towel-lined plate for 15–20 seconds. While still warm, roll each churro in cinnamon sugar until well coated.

Serve: Enjoy immediately with chocolate sauce or dulce de leche. Churros are best hot and fresh.