Heat oven to 375 degrees F and arrange rack in middle.
Butter and flour a 9 1/2-inch cake pan.
Whisk together flour, salt, and baking soda to aerate and break up any lumps; set aside.
Cream sugar and butter by mixing with an electric mixer on medium speed until light in color and fluffy, about 5 minutes.
Add the vanilla extract and mix to combine.
Add the egg yolks, one at a time, mixing well after each addition.
Add the flour and mix until just incorporated (dont overmixthere will be a few lumps left).
Fold in the walnuts until just incorporated; set aside.
Beat the egg whites until they just reach firm peaks, then fold into the batter until just incorporated (its fine to leave a few pockets of egg whites).
Turn the batter into prepared cake pan and bake in the heated oven until a cake tester inserted into the outside edge of the cake comes out clean and the center is still slightly soft, about 20 minutes.