In a medium saucepan, combine the water, unsalted butter, Kosher salt, and the stick of cinnamon. Bring this mixture to a gentle boil over medium heat. The butter should melt completely.
Once boiling, remove the pot from the heat and add the all-purpose flour all at once. Stir vigorously with a wooden spoon until the dough comes together and pulls away from the sides of the pan. This should take about 1-2 minutes.
Let the dough cool for about 5 minutes, then add the lightly beaten egg and vanilla extract. Stir until the egg is fully incorporated, and the dough is smooth and slightly sticky.
In a heavy-bottomed pot or deep fryer, pour in enough vegetable oil to reach a depth of about 2-3 inches. Heat the oil to 350°F (175°C). Use a candy thermometer for accuracy.
While the oil heats, transfer the churro dough into a pastry bag fitted with a large star tip. You want the dough to be ready when the oil reaches the perfect temperature.
Once the oil is hot, carefully squeeze out strips of dough, about 4-6 inches long, into the oil. Fry only a few at a time to avoid overcrowding. Fry until golden brown, about 2-3 minutes on each side.
Using a slotted spoon, remove the churros from the oil and place them on a plate lined with paper towels to drain excess oil. In a separate bowl, combine the granulated sugar and ground cinnamon. Roll the warm churros in the cinnamon sugar mixture until well coated.
Serve the churros warm, with optional chocolate sauce for dipping. Enjoy your delicious Homemade Churros with family and friends!