In a shallow bowl, combine the ½ cup sugar and cinnamon. Set aside.
In a large saucepan or pot, add the water and the cinnamon sticks and bring to a boil over high heat for 2 to 3 minutes.
Remove the cinnamon sticks and turn the heat to low. Stir in the butter and vanilla. Continue cooking until the butter has melted, stirring frequently.
In a mixing bowl, combine 2 cups flour, brown sugar, baking powder and salt. Slowly stir the flour mixture into the water mixture. When the flour has been absorbed, remove the pan from the heat.
Stir in the eggs. Slowly stir in the flour until you get a thick, cookie dough consistency. Place the dough into a piping bag with a large open star piping nozzle attached.
Add the oil to a Dutch oven or cast iron skillet to about 1 ½ -inches deep. Heat to 350 degrees F. Pipe the dough into strands (about 6 to 8-inches long) in the fry oil. Fry about 2 to 3 minutes or until a light golden brown, rotating as needed.
Strain the dough from the oil and immediately place in the cinnamon sugar mixture and toss to generously coat. Place on a plate or wire rack. Best if served warm. Dip in the caramel coffee sauce, if desired.