Preparation:

Step 1: Prepare the Cake Batter

1. Preheat the oven to 350°F (175°C). Grease and flour two 9-inch round cake pans or line them with parchment paper.
2. In a medium bowl, whisk together the all-purpose flour, baking powder, baking soda, cornstarch, and salt. Set aside.
3. In a large mixing bowl, beat the softened butter and granulated sugar together until light and fluffy.
4. Add the eggs, one at a time, mixing well after each addition. Then stir in the vanilla extract and optional strawberry extract.
5. Mix in the pureed strawberries and sour cream until fully incorporated.
6. Gradually add the dry ingredients to the wet mixture, alternating with the buttermilk. Mix until just combined. Do not overmix.
7. If using, add a few drops of pink food coloring to enhance the color of the batter.
8. Divide the batter evenly between the prepared cake pans.

Step 2: Bake the Cake

1. Place the cake pans in the preheated oven and bake for 28-32 minutes, or until a toothpick inserted into the center comes out clean.
2. Remove the cakes from the oven and let them cool in the pans for about 10 minutes.
3. Transfer the cakes to a wire rack and let them cool completely before frosting.

Step 3: Prepare the Strawberry Cream Cheese Frosting

1. In a large bowl, beat the softened cream cheese and butter together until smooth and creamy.
2. Gradually add the powdered sugar, one cup at a time, beating well between each addition.
3. Stir in the vanilla extract, lemon juice, and salt.
4. Gently fold in the finely chopped or mashed strawberries. Be careful not to add too much liquid, or the frosting may become too thin.
5. If the frosting is too soft, chill it in the refrigerator for about 20 minutes before frosting the cake.

Step 4: Assemble the Cake

1. Place one cooled cake layer on a serving plate.
2. Spread a generous amount of frosting over the top.
3. Place the second cake layer on top and frost the entire cake, covering the sides and top evenly.
4. Use a spatula to create swirls or decorative patterns on the frosting.
5. Optionally, garnish with fresh strawberries on top.

Step 5: Chill and Serve

1. Refrigerate the cake for at least 30 minutes to help set the frosting.
2. Slice and serve the cake at room temperature for the best texture and flavor.