Heat oven to 375°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 (don’t overmix—there 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 (it’s 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. Serve hot or at room temperature.
Beverage pairing: Blandy’s Malmsey 5 Years Old Madeira, Portugal. A nut cake deserves a wine that has the essence of nuts in it, just like this young Madeira, which brings flavors of roasted nuts, spices, and molasses. It can be drunk chilled alongside the cake, or even poured over it.
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