Whisk eggs and vanilla in a small bowl. Add to the dough and stir until completely incorporated. Transfer the dough to a pastry bag fitted with a 3/4-inch open-star tip. (Alternatively, if using a 1-quart sealable plastic bag, fill it with dough and seal almost completely, leaving a small opening for air to escape from the top as you squeeze. Snip off a bottom corner, making a 3/4-inch-wide opening.) Pipe the dough onto the prepared baking sheet to make 12 churros, each 4 inches long.