Preheat the oven to 350°F. Brush the bottoms and sides of the pans with melted butter. Line the bottoms with parchment paper; grease the paper.
In a large bowl, mix together the cake flour, all-purpose flour, baking powder and the salt. Set aside.
In the bowl of a stand mixer fitted with the paddle attachment, beat the butter and sugar on medium-high speed until light and fluffy. Add the vanilla and mix in. Turn the mixer to its lowest speed and gradually add the egg whites, scraping the bowl often. In a separate bowl, mix the milk and strawberry puree together. Alternately add the flour mixture and milk mixture to the creamed butter and sugar, starting and ending with the flour. Scrape the bowl after each addition, and beat thoroughly until combined. Divide the batter evenly between the cake pans. Bake approximately 40-45 minutes, or until a toothpick inserted in the center comes out clean. Cool the pans on racks for 20 minutes. Run a spatula around the perimeter to release the cakes. Turn them from their pans onto racks, remove the paper and cool completely.
A good time to prepare the strawberry syrup is while the cakes are baking. Combine the sugar, water and strawberry puree in a small saucepan and whisk until the sugar is incorporated but still granular. Bring to a boil over high heat without stirring. When the sugar comes to a boil, remove from heat and cool completely.
Make the buttercream. In the bowl of a stand mixer, whisk together the sugar and egg whites until well combined. Set the bowl over a pot of boiling water and whisk constantly. While whisking, heat the mixture until all the sugar granules have dissolved and the mixture is hot to the touch. Aim for getting the mixture as hot as possible but don’t overcook it into scrambled eggs.
Return the bowl to the mixer and seat the whip attachment. Beat on high speed until the meringue thickens and forms stiff glossy peaks, about 10 minutes. The bottom of the bowl should be at or close to room temperature. Stop the mixer and replace the whip with the paddle attachment. Set the mixer on low speed and add the butter, a few cubes at a time. After all the butter has been incorporated, beat the frosting on medium speed until fluffy.
Set the mixer back to low speed and add the vanilla, strawberry puree and jam. Once everything is incorporated, scrape the bowl down and continue to mix until a smooth, creamy texture is reached. If the frosting is too liquid, place in the refrigerator until thoroughly chilled and firm, then re-whip. If the frosting appears broken, beat on high for 3 to 5 minutes more and it will come together.
Assemble the cake. Place the first layer on a serving plate, brushing the top with the strawberry syrup. Place a large dollop of frosting on top and spread evenly to within ¼ inch of the edge. Place the 2nd layer on top, brushing its top with the syrup. Frost this layer as you did the last. Now place the final layer over top and brush the top again with syrup. Frost the top and sides with a thin crumb coat. Place the cake in the refrigerator to firm the coating. Finish frosting the top and sides of the cake reserving a small amount to use for borders. When the cake is frosted pipe a decorative border at the base and at the top edge. As an added touch, make your cake dainty with some sprinkles on top.
Fresh berries yield superb flavor and color to baking—choose ones that are fragrant, ripe and red. You may substitute frozen berries provided they are the whole, quick-frozen variety. Just thaw them and puree. If use you frozen berries with added sugar, then adjust the sugar accordingly in the frosting or it may be too sweet. In the event you are unfamiliar with Swiss-meringue buttercreams, take it step-by-step and follow the tips if the process goes awry. The pasteurized egg whites in liquid form found in cartons at the grocery store are convenient and saves time.