Preheat the oven to 350. Butter and flour a 9-inch cake pan. Combine the egg yolks and 3/4 cup of sugar in a mixing bowl, and whisk until thick and light in color. Stir in the vanilla. Beat the egg whites and salt with an electric mixer until they form soft peaks. Add the remaining 2 tablespoons sugar, and beat until glossy, 15 to 20 seconds more. Incorporate 1/3 of the whites into the egg mixture. Combine the flour and the ginger, mix well. Then sift 1/4 cup of flour mixture over the egg mixture, and gently fold it in with a spatula. Repeat, folding in whites and flour mixture until the last of the batch of flour is nearly incorporated. Then fold in the melted butter. Pout the batter into the prepared pan, and bake just until the cake begins to pull away from the sides of the pan, about 30 minutes. Cool 10 minutes in the pan and remove from the pan.
Whip the sugar and cream until soft peaks form. Remove the cake from the pan, and place on a pretty plate. Using a pastry brush, moisten the cake with the ginger syrup. Fold the finely chopped ginger into the whipped cream, and ice the cake with the cream. Decorate with candied ginger and mint. Dust with powdered sugar.