Lightly toss sliced strawberries with 2 Tbsp sugar, put on a strainer and let sit for a couple of hours. After waiting time, use a food processor or blender to puree strawberries to a fine mix. Reserve 3/4 cup of puree. Collect the drippings on a pan,add 1/2 cup sugar and the rest of puree, reduce to half simmering over low-medium heat, stir to prevent sticking to the bottom. Set puree and "jam" aside, don't refrigerate!
Preheat oven to 350 F, grease and line with parchment paper 2 x 8" pans, if possible use Bake-Even straps or line outside with a stripe of folded heavy duty aluminum foil.
Wisk strawberries puree, milk, egg whites and extracts, until blended.
Put flour, sugar, baking powder and salt in mixer's bowl and mix 1 minute in low to mix well dry ingredients. Add butter one tablespoon at a time, keep mixing untill all butter is combined and mixture resembles crumbs.
Add liquids in a slow flow while beating to combine evenly. Stop, scrape the sides and hand beat 30 more seconds (be carefull not to overbeat). Divide batter among pans and smooth tops.
Bake for 25-30 minutes, test for done on the center, should not separate from sides while still in the oven. Let cool 10 minutes on wire rack and un-mold. Let cakes cool completely (2 hours) before assembling.
Cover top of one layer and bottom of the other with room temperature strawberry jam. Place the layer with the jam-covered top on a serving plate, spread buttercream and put the jam-covered bottom cake on top.
Cover the cake with vanilla buttercream or, if so desired, mix the rest of the jam with buttercream and use this to ice the cake.