Preheat the oven to 350°F (175°C). Grease and flour two 9-inch round cake pans, or line the bottoms with parchment.

Puree 1 cup fresh strawberries in a blender or with an immersion blender until smooth. Measure out 1 cup for the batter and reserve 1/4 cup for the frosting.

In a large bowl, cream 1/2 cup softened butter and 1 1/2 cups sugar until light and fluffy (about 3–4 minutes with a hand mixer).

Beat in the eggs, one at a time, scraping the bowl after each addition. Stir in 1 teaspoon vanilla and the 1 cup strawberry puree.

In a separate bowl, whisk together 2 cups all-purpose flour and 2 teaspoons baking powder.

Add the dry mixture to the wet mixture in three additions, alternating with 1 cup milk (dry, milk, dry, milk, dry). Mix just until combined — do not overmix.

Divide the batter evenly between the prepared pans and smooth the tops with a spatula.

Bake for 25–30 minutes. A toothpick inserted in the center should come out clean or with a few moist crumbs.

Cool the cakes in the pans on a wire rack for 10 minutes. Run a knife around the edges, invert onto the rack, remove parchment, and cool completely before frosting.

For the frosting, beat 1/2 cup softened butter until creamy.

Gradually add 4 cups powdered sugar, alternating with the reserved 1/4 cup strawberry puree, and beat until smooth and spreadable.

Add 1 teaspoon vanilla and mix. If frosting is too thin, add a little more powdered sugar; if too stiff, add a teaspoon or two of milk.

Place one cake layer on a serving plate. Spread a thin, even layer of frosting on top. Place the second layer on top and frost the top and sides.

For a neater finish, do a thin “crumb coat,” refrigerate 15–20 minutes, then finish with the final layer of frosting.