1 cup plus 2 tablespoons all-purpose flour
1 tablespoon cinnamon
1 cup water
2 tablespoons brown sugar
2 tablespoons vegetable oil
1/4 teaspoon salt
2 large eggs
Oil, for frying
1 cup granulated sugar
9 scoops dulce de leche ice cream
Make the churro cookies: Sift together the flour and 1 teaspoon of cinnamon into a medium mixing bowl.
Add the water, brown sugar, vegetable oil, and salt to a medium saucepan set over medium heat. Bring to a boil, and once boiling, add in the flour mixture, and stir quickly. The mixture will be thick, but continue to stir it until the flour is incorporated and it forms a rough, shaggy ball of dough.
Transfer the dough to the bowl of a stand mixer fit with the paddle attachment. Beat on medium speed and add eggs one at a time until the dough is combined and smooth.
Line two baking sheets with parchment or wax paper. Fit a pastry bag with a #821 piping tip, and fill bag with churro dough. Pipe the dough into 3-inch circles, starting at the center of the circle and working outward in a spiral pattern. Keep the tip close to the baking sheet so the dough is thin. You should get about 18-20 circles from one batch. Place baking sheets in the freezer for at least 10 minutes to set and chill the dough.
While the churros are freezing, heat the oil for frying. Add oil to a large skillet or deep fryer so that it's at least 2 inches deep. Heat the oil to 350ºF. Line a baking sheet with several layers of paper towels. In a medium-sized bowl, mix together the granulated sugar and remaining 2 teaspoons of cinnamon.
Fry 2-3 churros at a time, turning them over occasionally so they brown evenly. When they are finished they will be slightly puffed and golden brown on both sides. Transfer them to the paper-towel-lined baking sheet using a slotted spoon or spatula to let the oil drain. Quickly toss them in the cinnamon sugar mixture while they are still warm. Continue working in small batches until all of the churros are fried.
Make the churro ice cream sandwiches: Take one churro, top with a scoop of ice cream, and place another churro on top. Gently press together to adhere the cookies to the ice cream. Serve immediately, or freeze for later.