Melt the butter and let it cool slightly. Beat the egg whites with salt until soft peaks form. Gradually add the powdered sugar, beating until stiff but not dry.
In a separate bowl, beat the egg yolks slightly. Add the sugar and vanilla, and beat until thick and creamy. Sprinkle the flour over the egg whites. Add the egg yolks and gently fold until the mixture is half blended. Add the butter and 3/4 cup of the walnuts. Fold just until mixed. This is delicate, and it is important not to overmix.
Pour into a well buttered and floured 2-1/2 or 3 quart cake mold, or a 10-inch tube pan. Top with the remaining walnuts and bake at 350° for 40 minutes. The torte should bounce back when you touch it.
Cool the torte for 10 minutes in the pan. Then pierce the cake in several places with a long skewer and pour the rum sauce over the torte. This will take 10 minutes of on-and-off pouring to absorb the sauce. Place on a serving plate.