Preheat oven to 350 F. Line bottom of 8-inch springform pan with 2-3/4-inch high sides with parchment paper. Spread pan and paper with vegetable oil spray. Sprinkle pan with 2 tablespoons sugar. Finely grind nuts with 2 tablespoons sugar in processor. Transfer nut mixture to large bowl. Mix in 10 tablespoons sugar and cocoa, then oil.
Using electric mixer, beat egg whites and salt in large bowl until soft peaks form. Fold whites into cocoa mixture in 3 additions. Spoon batter into prepared pan; smooth top.
Bake until cake puffs and tester inserted into center comes out with moist crumbs attached, about 30 minutes. Cool cake in pan on rack about 30 minutes. (Cake may fall.) Cut around pan sides to loosen cake. Remove sides of pan and cool cake completely. Sprinkle cake with powdered sugar.