Preheat the oven to 350°F and prepare three cake pans by greasing and lining them with parchment paper so the cakes release easily after baking.
Blend the freeze-dried strawberries into a fine powder, then mix it with flour, sugar, baking powder, and salt until evenly combined.
In a separate bowl, whisk together milk, egg whites, oil, vanilla extract, and vinegar until smooth and well combined.
Gradually add softened butter into the dry mixture and mix until the texture becomes crumbly with no large butter pieces remaining.
Slowly add part of the liquid mixture to form a thick paste, then continue adding the remaining liquid while mixing until the batter becomes smooth, fluffy, and airy.
Divide the batter evenly into the prepared pans and bake until the tops spring back lightly and a tester comes out with a few moist crumbs.
Beat butter and cream cheese together until smooth, then add strawberry powder, salt, powdered sugar, and cream until the frosting becomes light and fluffy.
Prepare the optional syrup by heating water and sugar until dissolved, then mixing with strawberry puree once cooled.
Assemble the cake by leveling layers, brushing with syrup if using, frosting between layers, and finishing with frosting on top and sides before garnishing.
