In a saucepan over medium heat, melt the butter and brown sugar in the water and bring to a boil.
3. Step
Turn off the heat and stir in the flour.
4. Step
Take the pot off of the heat source, and mix in the vanilla, then the eggs one at a time.
5. Step
Transfer mixture to a piping bag with a 5 point, or star, tip.
6. Step
Pipe out thick 3-inch (8 cm) strips of churro batter onto a baking sheet covered with parchment, using a knife to release each piece from the piping tip, if needed.
7. Step
Bake for 10 minutes, then broil until golden brown.
8. Step
Dredge each churro in melted butter, then cinnamon sugar.