In a medium saucepan, combine the room temperature water, granulated sugar, salt, and salted butter. Heat over medium heat until the butter is melted and the mixture comes to a gentle boil. Remove from heat and stir in the vanilla extract.
Add the all-purpose flour to the saucepan, stirring vigorously with a wooden spoon until a dough forms. It should be smooth and pull away from the sides of the pan. Allow the dough to cool for about 5 minutes.
Once the dough has cooled slightly, add the large egg and mix thoroughly until it is fully incorporated. The dough should be smooth and somewhat sticky.
In a deep frying pan or pot, pour in enough vegetable oil to reach a depth of about 2 inches. Heat the oil to 350°F (175°C). Use a deep-frying thermometer to ensure the oil reaches the right temperature.
Transfer the dough to a pastry bag fitted with a star tip. Once the oil is hot, carefully pipe strips of dough into the hot oil, cutting them to your desired length with scissors. Fry the churros in batches to avoid overcrowding the pan.
Fry the churros for about 2-3 minutes on each side or until they are golden brown and crispy. Use a slotted spoon to remove them from the oil and place them on paper towels to drain excess oil.
In a shallow bowl, combine the granulated sugar and ground cinnamon. While the churros are still warm, roll them in the cinnamon sugar mixture to coat them evenly.
Serve your freshly made churros immediately, either plain or with a side of chocolate sauce for dipping. Enjoy the crispy, sweet, and cinnamon-scented goodness!