Preheat oven to 350ºF.
In a medium bowl, combine unsweetened cocoa, boiling water, vanilla and food coloring; whisk and set aside.
In another medium bowl, combine salt, 3/4 cup of sugar and cake flour; mix well and set aside.
Using an electric mixer, in a large bowl, beat egg whites until foamy. Add vinegar; continue to beat until soft peaks form. With electric mixer running on slow speed, gradually add remaining cup of sugar; increase to high speed and beat until stiff peaks form.
Remove a heaping cup of egg whites and add it to chocolate mixture; gently combine and set aside.
Sift flour mixture over egg whites, a little at a time, and fold after each addition to incorporate. Add chocolate mixture and gently fold into egg whites. When just combined, turn batter into a two-piece 10-inch angel food cake pan with feet; smooth top into an even layer.
Bake until a toothpick inserted in center of cake comes out clean, about 40 to 45 minutes. Remove cake from oven and invert pan onto its feet so the inverted cake can cool properly (the cake will not fall out of the pan). If your pan does not have feet, invert it over the neck of a wine bottle or a glass soda bottle.
When cake is completely cool to the touch, loosen edges with a sharp knife and remove cake from pan. Slice into 16 pieces and serve. Yields 1 piece per serving.