*For the strawberry puree, clean and remove the stems on about 1 quart of strawberries. Cut them in half and place them in a food processor to blend them into a puree. You should end up with about 3 cups of strawberry puree.
Place the strawberry puree in a small saucepan. Cook over medium-low heat, stirring often to prevent burning, until the strawberries have reduced to 1 1/2 cups of puree. I've found this to take about 30-45 minutes.
Allow the reduced strawberry puree to cool completely. (I often make this a day in advance so it has plenty of time to cool.)
For the Cake:
Preheat the oven to 350 degrees.
Sift together the cake flour, baking powder, soda and salt into a medium size bowl. Set aside.
In the bowl of stand mixer, cream together the softened butter and sugar.
Add the milk, oil and extracts. Beat on medium speed for 2minutes.
Add the reduced strawberry puree and egg whites. Beat for an additional 2 minutes.
Add the flour mixture and stir until well combined, but be careful not to overmix. Scrape the sides of the bowl as needed.
Grease and flour two 9" round cake pans. Divide the batter between the cake pans.
Bake at 350 degrees for 25 minutes, or until the cake springs back when you touch the center of it. Allow the cakes to sit for 5 minutes, then remove them from the pans to a wire rack to cool completely.
For the Buttercream:
In a stand mixer bowl, with the mixer on medium speed, whip the butter for 2-3 minutes until it is almost white in color. Add in the salt, powdered sugar, vanilla extract. Mix on low speed until blended. Add in the reduced strawberry puree, 1/4 a cup until the frosting is the consistency you'd like. Add a drop or two of red food coloring if you'd like the cake to be a little pinker. Beat on low speed again for 1-2 minutes.
Assemble the Cake:
Frost the top of one of the round cakes, then place the second cake on top of that.
Frost the entire outside of the cake with the strawberry frosting, making it as smooth as possible.
Decorate the top with cut or whole strawberries, if desired.
Cover and refrigerate until serving.
**We updated this recipe January 13, 2019 based on reviewers feedback. We've re-tested this recipe about 5 times and find that it rises better and is fluffier based off these instructions. We so appreciate your feedback!You can make this recipe into a 9x13 cake. Simply bake at the same time and temperature, watching it closely until the center of the cake springs back when you touch it. If you'd like less frosting, try:2 sticks of butter1/4 teaspoon salt4 cups powdered sugar1 teaspoon vanilla1 cup strawberry puree (added slowly until the frosting is at the correct consistency.)Make as directed above.