Working with a stand mixer fitted with the paddle attachment, or in a large bowl with a hand mixer, beat the butter, sugar and salt together on medium speed until smooth and creamy, about 3 minutes. Reduce the mixer speed to low and blend in the egg whites, followed by the vanilla. The dough might curdle, but it will smooth out with mixing and the addition of the flour. Still working on low speed, add the flour in 3 or 4 additions, beating only until it is almost incorporated each time before adding more; scrape down the sides and bottom of the bowl a couple of times as you work and then continue to mix until the flour has disappeared into the dough.