In a small bowl combine flour and 1 teaspoon of the cinnamon.
In a medium saucepan combine next 4 ingredients (through salt). Bring to a boil, add flour mixture. Stir immediately until a dough forms (mixture will be very thick). Remove from heat. Beat in eggs, one at a time.
Transfer dough to a pastry bag fitted with a small open star tip. Pipe 3- to 4-inch flat swirls on a wax paper lined cookie sheet. Freeze dough on cookie sheet until ready to use.
Add 2-inches of oil to a large deep skillet and heat to 350 degrees F. In a shallow dish combine sugar and remaining 2 teaspoons of cinnamon.
Working in batches, fry cookies until puffed and golden brown. Transfer cookies to a paper-towel lined plate to drain. While cookies are still warm, toss in cinnamon-sugar mixture.
Place 1 scoop vanilla ice cream on top of 1 churro cookie, top with another cookie.