Preheat the oven to 350°F (175°C)
Grease and flour two 8-inch cake pans
In a bowl, whisk together 2 cups all-purpose flour, 2 teaspoons baking powder, and 1/2 teaspoon salt
In another bowl, beat 1/2 cup softened butter and 1 1/2 cups sugar until light and fluffy
Add 2 eggs and 1 teaspoon vanilla extract, then mix well
Add 1/2 cup milk and 1/2 cup strawberry puree, then mix until combined
Gradually add the dry ingredients to the wet ingredients and mix until smooth
Divide the batter evenly between the prepared pans
Bake for 25 to 30 minutes
Let the cakes cool in the pans for 10 minutes
Remove the cakes from the pans and cool completely on a wire rack
For the frosting, beat 1/2 cup softened butter until creamy
Add 3 to 4 cups powdered sugar, 1/4 cup strawberry puree, and 1 teaspoon vanilla extract
Mix until smooth and spreadable
Place one cake layer on a plate and spread frosting on top
Add the second layer and frost the top and sides
Decorate with sliced strawberries if desired