In a large mixing bowl, combine cake mix, oil, eggs and sour cream. Stir by hand approximately 50 strokes, or until most large lumps are gone.
Pour half of the batter into an ungreased 9x13 inch glass baking dish.
Combine the brown sugar and cinnamon, and sprinkle over the batter in the cake pan. Spoon the other half of the batter into the cake pan, covering the brown sugar and cinnamon. Twirl the cake with a butter knife or icing knife until it looks like a honey bun (or whatever design you want to make).
Bake in preheated oven for 40 minutes, or until a toothpick inserted into the center of the cake comes out clean.
Frost cake while it is still fairly hot.
To Make the icing: In a small bowl, whisk together the confectioner's sugar, milk and vanilla until smooth.