Make the cake: Preheat the oven to 350 degrees F. Sift the flour, confectioners' sugar and salt onto a sheet of parchment paper. Sift again, then set aside.
Beat the egg whites in a large bowl with a mixer on medium speed until frothy. Add the cream of tartar and beat until soft peaks form, about 5 minutes. Gradually beat in the granulated sugar, about 1 tablespoon at a time, then increase the speed to medium high and continue beating until stiff, shiny peaks form, 12 to 15 minutes. Add the vanilla, lime zest and ginger and beat a few seconds to combine.
Sprinkle one-quarter of the flour mixture over the egg mixture and gently fold with a rubber spatula. Fold in the remaining flour mixture in 3 additions. Transfer the batter to an ungreased 10-inch tube pan. Bake until the cake feels springy and a toothpick inserted into the center comes out clean, 40 to 50 minutes. Invert the pan onto a funnel or the neck of a bottle and cool completely. Loosen the edges with a small knife, tap the sides of the pan against the counter and unmold.
Make the sauce: Puree 2 half pints raspberries in a blender with 2 tablespoons water, the granulated sugar, lime zest and lime juice. Strain to remove the seeds. Top the cake with confectioners' sugar, the sauce and the remaining raspberries.