Make the cake: Preheat the oven to 375 degrees F. On a sheet of waxed paper, sift the cake flour with 3/4 cup of the sugar and the cocoa 4 times.
Using an electric mixer fitted with the whisk attachment, beat the egg whites along with a pinch of salt until foamy, about 3 minutes. Sprinkle the cream of tartar over the egg whites and continue to beat until they hold a soft peak, about 5 minutes. Beating continuously, add the vanilla and gradually stream in the remaining 3/4 cup sugar, about 2 tablespoons at a time, until the egg whites are thick, glossy and stiff.
Remove the bowl from the mixer, and using a spatula, gradually fold in the flour mixture, about 1/4 cup at a time, until there are no more pockets of dry ingredients. Spoon the batter into an ungreased 9-inch tube pan. Bake until the cake springs back when pressed with your finger, about 30 minutes. Remove the pan from the oven, invert, and allow the cake to cool on a rack 1 hour before loosening the cake from the pan with a knife and unmolding.
Meanwhile, make the strawberries: Sprinkle the sliced strawberries with the sugar. Stir to coat and let stand about 30 minutes to allow the juices to develop. Top each cake slice with strawberries and their juices before serving.