Preheat oven to 375°F Spray a 9x13 inch baking pan with cooking spray.
Combine brown sugar, cinnamon, and butter in small bowl, set aside.
Separate breadsticks into 12 strips. Sprinkle tops with brown sugar mixture and roll each one into a spiral, pressing to seal the ends. Arrange in baking pan 1 inch apart. Bake until lightly golden, about 15-18 minutes. Cool for 10 minutes.
To prepare frosting, combine confectioners sugar, cream cheese, and vanilla in a small bowl, adding a few drops of water if needed to make a smooth, spreadable glaze. Drizzle over the tops of the warm rolls and let stand a few minutes to set. Serve warm.