Preheat your oven to 350°F (175°C). Grease a 9x13-inch baking dish and set aside.
In a large bowl, mix together the cake mix, oil, eggs, and sour cream until smooth. Do not overmix.
Pour half of the cake batter into the prepared dish. In a small bowl, combine brown sugar and cinnamon. Sprinkle half over the batter.
Add the remaining cake batter, then top with the rest of the cinnamon sugar mixture. Use a knife to gently swirl the layers together.
Bake for 35–40 minutes, or until a toothpick inserted in the center comes out clean. Let the cake cool slightly.
Meanwhile, prepare the icing by whisking together powdered sugar, melted butter, vanilla, strawberry puree, and enough milk to reach a pourable consistency.
Drizzle icing generously over the warm cake and allow it to soak in before serving.