In a saucepan, combine water, butter, sugar, and salt. Heat the mixture until it comes to a gentle boil, then reduce the heat to low and stir in the flour. Cook while stirring until the dough forms a smooth ball and pulls away from the sides of the pan. Remove the dough from the heat and let it cool for a few minutes.
Next, stir in the egg and vanilla extract until the mixture is smooth and sticky. Transfer the dough to a piping bag fitted with a large star tip.
Heat 2 inches of vegetable oil in a deep pot to 350°F (175°C). Carefully pipe 4- to 5-inch strips of dough into the hot oil, using scissors to snip each piece. Fry a few churros at a time, turning occasionally, until golden brown (about 3-4 minutes). Remove with a slotted spoon and drain on paper towels.
In a shallow bowl, mix granulated sugar and ground cinnamon. While the churros are still warm, roll them in the cinnamon-sugar mixture until fully coated.
Combine chocolate chips and heavy cream in a microwave-safe bowl. Heat in 20-second intervals, stirring after each, until smooth. Serve the sauce warm as a delicious dipping option.