Preheat oven to 325 degrees and spray a 9x13-inch baking dish with cooking spray.
In a large bowl, stir together cake mix, eggs, vegetable oil, and sour cream until smooth.
Pour half of cake batter into prepared pan and smooth it out.
Stir together brown sugar and cinnamon in a bowl. Sprinkle evenly on top of cake batter.
Cover with remaining cake batter, spreading it evenly. Run a knife in a swirling pattern through the cake batter.
Bake 30 to 35 minutes.
In a medium bowl, whisk together powdered sugar, milk, and vanilla. Pour over hot cake. Let cake cool 20 minutes before cutting.