Preheat the oven to 350°F. Butter and lightly flour two 8-inch round cake pans. Put the cocoa, 3 tablespoons of the sugar, and 3 tablespoons water in a small pan and cook over low heat until smooth and blended. Remove from the heat and stir in the milk; set aside.

Cream the butter or shortening, add the vanilla and 1/2 cup of the remaining sugar, and beat until light. Beat in the egg yolks, and then add the cocoa mixture, beating well.

Mix the flour, cream of tartar, salt, and baking soda together, add to the first mixture, and blend until smooth. Beat the egg whites separately until they are foamy, slowly add the remaining 1/2 cup of sugar, and continue to beat until the whites are stiff but not dry. Fold the whites into the batter.

Spread in the pans and bake for 25 - 30 minutes; test with a toothpick until it comes out clean. Cool in the pans for 5 minutes before turning out onto racks.