Begin by preparing your cake base, which forms the foundation of this delicious dessert. Sift together 1 1/2 cups flour, 3 tablespoons cornstarch, 1/2 teaspoon salt, and 1 teaspoon baking soda in a bowl and set aside. In a separate large mixing bowl, cream 9 tablespoons softened butter with 1 1/2 cups sugar until the mixture becomes light and airy. Add 3 large eggs one at a time, mixing well after each addition to facilitate proper incorporation.
Next, blend in 1/2 cup room temperature sour cream and 1 teaspoon vanilla until just combined. Gradually add the sifted dry ingredients, mixing on low speed until barely combined - avoid overmixing to maintain a tender crumb. Pour the batter into a greased and floured 8-inch pan and bake at 350°F for 45 minutes. Remove the cake from the pan immediately upon taking it out of the oven and allow it to cool completely before proceeding.
While the cake cools, prepare your strawberry filling by slicing 1 lb of fresh strawberries and sprinkling them with 3 tablespoons sugar. Mash the strawberries lightly with a fork and let them sit for 5-10 minutes to release their natural juices.
Once the cake has cooled, carefully slice it in half horizontally to create two layers. Spread the macerated strawberries over the bottom layer, but resist placing the top layer on immediately. Instead, place the strawberry-topped bottom layer in the refrigerator or freezer for about 30 minutes while you prepare the frosting - this chilling step makes the final assembly and frosting process much easier.
For the cream cheese frosting, cream together 1/2 lb room temperature cream cheese and 1 cup room temperature butter until smooth. Gradually add 1 1/2 lbs sifted powdered sugar, 1 teaspoon vanilla, and a dash of salt, mixing until the frosting becomes light and airy.
Remove the chilled cake from the refrigerator and spread slightly less than one-third of the frosting over the strawberry layer. Gently place the top cake layer over the frosted strawberries, then spread the remaining frosting over the entire cake.
The finished cake can be left plain or garnished with additional sliced strawberries, but should be served slightly cold since the frosting will soften at room temperature - store in the refrigerator between servings.