Preheat the oven to 350°F. Grease a 9x13-inch pan.
In a small bowl, mix brown sugar and cinnamon. Set aside.
In a large bowl, whisk together cake mix, eggs, sour cream, butter, vegetable oil, water and extract until smooth.
Pour half of the batter into the prepared pan. Sprinkle the brown sugar mixture over the batter, then dollop the remaining batter on top. Using a knife, insert it half ways into the batter and swirl back and forth along the cake.
Bake for 32-35 minutes, or until lightly golden brown (a toothpick inserted in the middle should come out clean).
While cake is baking make icing, by mixing all the ingredients in a medium bowl, beating until smooth.
While the cake is still warm, poke cake with a popsicle stick (or the back end of plastic fork) all over the cake. Pour the icing over the warm cake and spread. Let set up for at least 15 minutes before serving.