Make the cinnamon sugar. In a shallow dish, mix 1/2 cup granulated sugar with 1–2 teaspoons ground cinnamon. Set aside for rolling the hot churros.
Heat the oil. Pour 2 inches of neutral oil into a heavy pot. Heat to 360–370°F (182–188°C).
Keep a thermometer clipped to the side for steady temperature.
Start the dough. In a medium saucepan, combine water, butter, 2 tablespoons sugar, and salt. Bring to a gentle boil over medium heat, stirring to melt the butter.
Add the flour. Turn the heat to low. Add flour all at once and stir vigorously with a wooden spoon until the mixture pulls away from the pan and forms a smooth ball, about 1–2 minutes.
A thin film on the pan is normal.
Cool slightly. Transfer the dough to a bowl. Let it cool for 5 minutes so the eggs don’t scramble.
Beat in eggs and vanilla. Add the vanilla. Beat in the eggs one at a time, mixing until glossy and smooth after each.
The dough will look split at first—keep mixing until it comes together and is pipeable.
Prepare to pipe. Fit a piping bag with a large open star tip (such as 1M or 827). Spoon in the dough. If you don’t have a piping bag, use a sturdy zip-top bag with a corner snipped; ridges will be less defined but still tasty.
Test fry. Pipe a 3–4 inch strip of dough onto a small piece of parchment or directly over the pot, cutting with scissors.
Fry 1–2 churros to test timing: about 2–4 minutes, turning once, until deep golden.
Fry in batches. Pipe 4–6 strips at a time, depending on pot size. Don’t crowd the oil. Fry until golden and crisp, turning occasionally for even color.
Keep the oil within the 360–370°F range; adjust heat as needed.
Drain and coat. Remove churros to a paper towel–lined tray for 10–15 seconds, then roll while still hot in the cinnamon sugar. The warmth helps the sugar cling.
Optional chocolate dip. For a quick sauce, heat 1/2 cup heavy cream until steaming. Pour over 4 oz chopped dark chocolate, wait 1 minute, then stir until smooth and glossy.
Serve immediately. Churros are best hot and fresh, with a crisp shell and soft middle.