In a medium bowl or liquid measuring cup, whisk together the milk, egg whites, crème fraiche, and vanilla. In the bowl of a stand mixer fitted with a paddle, combine the flour, granulated sugar, baking powder, and salt. With the mixer running on low speed, add the butter one piece at a time, beating until the mixture resembles coarse sand. With the mixer still running on low speed, slowly add a little more than half of the wet ingredients. Increase the speed to medium and beat until the ingredients are incorporated, about 30 seconds. Lower the speed to low and add the rest of the wet ingredients, mixing until just combined. Increase the speed to medium and beat for 20 seconds (the batter may still look a little bumpy). Scrape down the sides and bottom of the bowl and use a spatula to mix the batter a few more times. Pour all but 1 tablespoon of the batter into the prepared pan and smooth the top.