In a shallow dish, whisk together 1/2 cup sugar and cinnamon, then set it aside for coating.

In a large pot or deep skillet, heat about 1 1/2 inches of vegetable oil over medium-high heat until it reaches 260°F. While the oil heats, melt the butter.

In a separate large saucepan, combine water, butter, sugar, and salt, and bring it to a boil over medium-high heat. Once boiling, add the flour, reduce the heat to medium-low, and stir constantly with a rubber spatula until the mixture is smooth (a few lumps are okay).

Transfer the dough to a large bowl and let it cool for 5 minutes.

Add the vanilla and egg to the dough, and immediately mix with an electric mixer. Blend until the dough is soft and smooth; it may look separated at first, but keep mixing, and it will come together.

Fill a piping bag fitted with a rounded star tip (no larger than 1/2 inch) with the dough. I recommend using an Ateco 845 or 846 tip.

Carefully pipe the dough into the preheated oil, cutting it into 6-inch lengths using clean scissors. Fry for about 2 minutes on each side until golden brown.

Transfer the churros briefly to paper towels to drain excess oil, then roll them in the cinnamon-sugar mixture until well coated.

Repeat with the remaining dough, frying no more than five at a time. Serve hot for the best flavor and texture!