Preheat the oven to 350°F (175°C). Grease the cake pans and line the bottoms with parchment paper.
In a large mixing bowl, combine the flour, sugar, baking powder, and salt.
Add the softened butter, milk, eggs, and vanilla extract to the dry ingredients. Mix using an electric mixer or whisk until you achieve a smooth batter.
Gently fold in the pureed strawberries until evenly distributed.
Divide the cake batter evenly between the two prepared pans.
Bake in the preheated oven for 25-30 minutes or until a toothpick inserted into the center comes out clean.
Once done, remove the pans from the oven and let them cool in the pans for about 10 minutes. Then, turn them out onto a cooling rack to cool completely.
While the cakes are cooling, prepare the frosting. In a mixing bowl, beat the softened butter until creamy.
Gradually add the powdered sugar, alternating with the pureed strawberries, mixing until smooth.
Add the vanilla extract and a pinch of salt to the frosting, mixing until combined.
Once the cakes are completely cool, spread a layer of frosting on top of one cake layer, place the second layer on top, and frost the top and sides of the entire cake.
Decorate with additional fresh strawberries, if desired, and slice to serve.