Keep the oven at 350 degrees F (as it was for roasting the strawberries). And grease a 13x9-inch baking pan. Set aside.
In a medium bowl, add the cake flour, baking powder and salt. Whisk until combined. Set aside.
To the bowl of a stand-up mixer with the paddle attachment, add the butter and sugar. Beat until light and fluffy, about 2 to 3 minutes. In a measuring cup, pour in the milk, egg whites, vanilla extract or paste and reserved 1/2 cup strawberry puree (discard any extra) and whisk until combined.
Turn the mixer to low speed and, alternating between the dry ingredients and the liquid ingredients (the strawberry/egg white mixture), add the them butter/sugar mixture until the batter is relatively smooth.
Pour the batter into the prepared baking pan and transfer to the oven to bake for 25 minutes, until a skewer inserted into the center comes out clean.
Allow the cake to cool in the pan for about 5 minutes and then invert onto a cooling rack and cool to room temperature. It’ll probably take a good hour.