In a wide dish, mix the granulated sugar and cinnamon and set aside.
In a medium saucepan, combine water, butter, brown sugar, and salt. Bring to a boil over medium heat, then add flour all at once, stirring vigorously with a wooden spoon. Cook and stir until mixture forms a ball and pulls away from the sides of the pan. Remove from heat. Cool for 10 minutes.
In a separate mixing bowl, mix together the eggs and vanilla extract. Add to the cooled flour mixture, beating well with a wooden spoon.
Fill a decorating bag fitted with a 1M large star tip with some of the churro dough. (The star tip helps create the ridges on the outside of the churro.)
On a baking sheet, pipe dough in 2-inch spirals. If necessary, freeze dough until firm enough to lift from the baking sheet.
Heat 2 inches of oil and the lemon peel in a deep saucepan to 375 degrees F. Try testing the oil by dropping in a small amount of dough. If it bubbles quickly then it is probably ready. If you have a candy thermometer test the temperature. (When lemon peel becomes crispy remove from oil and discard.)
As soon as your oil is hot enough, fry churros about 5 to 6 minutes or until puffed and golden brown, turning once.
Drain churros on a paper-lined plate. While churros are still warm and as soon as you are able to handle them, toss each one in the sugar-cinnamon mixture.
Cool completely on a wire rack.
Sandwich one small scoop lemon filling between two churros.