Place two cups of water, three-quarter cups of butter, and four tablespoons of white sugar in a saucepan and bring to a boil. Add two teaspoons of vanilla and remove from heat. To the pot, add in two cups of Bisquick, and stir until thickened. Set aside and allow to cool for twenty minutes.
With an electric hand mixer, beat in four eggs one at a time, until well blended. Spoon the mixture into a piping bag and use a star or large open tip.
Pour the oil into a pot or a deep fryer, and heat to three hundred and seventy-five degrees. Pipe the mixture carefully into the hot oil, resembling a rope shape to the desired length. Fry until golden brown, approximately three to five minutes, turning if needed.
Remove the churros with a slotted spoon and roll each one while still hot in cinnamon sugar. Place on a rack to cool. These can be stored in an airtight container for up to four days.