Preheat your oven to 350°F (175°C). Grease and flour a 9x13-inch baking pan.
In a large mixing bowl, combine the flour, sugar, vegetable oil, eggs, buttermilk, vanilla extract, baking powder, baking soda, and salt. Mix until well combined and smooth.
In a small bowl, mix the brown sugar and cinnamon together for the swirl.
Pour half of the cake batter into the prepared baking pan. Sprinkle half of the cinnamon-sugar mixture over the batter. Add the chopped strawberries evenly on top. Pour the remaining batter over the strawberries and sprinkle the rest of the cinnamon-sugar mixture on top.
Using a knife, gently swirl the batter to create a marbled effect.
Bake in the preheated oven for 40-45 minutes, or until a toothpick inserted into the center comes out clean. Allow the cake to cool completely in the pan.
For the icing, whisk together the powdered sugar, milk, and pureed strawberries in a small bowl until smooth.
Once the cake is cool, drizzle the creamy strawberry icing over the top.