In a shallow bowl, mix together ½ cup sugar and the cinnamon.
Heat a medium saucepan over medium heat. Add the water, butter, and vanilla. Bring to a simmer, stirring to combine all ingredients, for about 3 minutes or until the sugar is dissolved. Remove the saucepan from the heat and stir in the flour. Then, let cool to room temperature, about 5 minutes.
While cooling, heat the oil: In a medium deep saucepan or pot over medium heat, add enough oil to fill about 1-1 ½ inches deep in the pan. Heat to 350-370 degrees Fahrenheit, using a thermometer and adjusting the temperature as necessary to stay in this range.
Once the dough is cooled to the touch, add one egg at a time, beating with an electric mixer, until fully incorporated. Fit a piping bag with a star tip, then fill with the dough.
Carefully pipe 4-5 inch long pieces of dough into the hot oil, cutting the end of each section with scissors to separate the dough from the piping bag. Fry 3-4 churros at a time for about 4 minutes or until golden brown, rotating halfway through.