Sift cake flour and measure 1/2 cup. In a bowl, mix flour, 1/4 cup sugar, cocoa, instant espresso, and salt.
In a deep bowl (at least 4-qt.) with a mixer at high speed, whip egg whites and cream of tartar until they form a thick foam. Continue to beat and add remaining 1 cup sugar, 1 tablespoon about every 15 seconds, whipping until whites hold very stiff peaks.
Mix in vanilla.
Sprinkle about 1/2 the flour mixture over whipped whites. Gently fold mixture until blended.
Sprinkle with remaining flour mixture and gently fold to blend well. Scrape batter into a 10-inch tube cake pan with a removable rim; spread level.
Bake in a 350 oven until center of cake springs back when lightly pressed and begins to pull from pan side, 40 to 45 minutes.
Invert pan on a rack; let stand at least 1 hour. Run a thin knife between cake and pan rim. Push cake from pan rim. Slide thin knife between cake and pan bottom, and around tube to pan bottom. Invert cake onto a plate and lift out tube section.