Preheat the oven to 350°F (175°C). Grease and flour a 9×13-inch sheet cake pan.
In a medium bowl, whisk together the all-purpose flour, baking powder, and salt. Set aside.
In a large bowl, beat 1 cup softened butter and granulated sugar together with an electric mixer on medium speed until light and fluffy, about 3-4 minutes.
Add the eggs one at a time, beating well after each addition. Stir in 1 teaspoon vanilla extract.
Alternately add the flour mixture and whole milk to the butter mixture, beginning and ending with the flour mixture. Mix just until combined.
Fold in 1 cup pureed fresh strawberries gently until evenly incorporated.
Pour the batter into the prepared sheet cake pan and smooth the top with a spatula.
Bake for 28-30 minutes, or until a toothpick inserted into the center comes out clean.
Remove the cake from the oven and let it cool completely in the pan on a wire rack.
While the cake cools, prepare the frosting: In a large bowl, beat 1 cup softened butter until creamy.
Gradually add powdered sugar, 1 cup at a time, beating on low speed until combined.
Add 1/4 cup pureed fresh strawberries, 1 teaspoon vanilla extract, and 2 tablespoons heavy cream. Beat on medium-high speed until light and fluffy, about 3-4 minutes.
Once the cake is completely cooled, spread the strawberry frosting evenly over the top.
Arrange 2 cups fresh sliced strawberries decoratively on top of the frosting.
Cut into 12 squares and serve.