1. Heat the oven to 350 degrees. Toast the walnuts on a baking sheet until fragrant and lightly colored, about 10 minutes. Cool completely. Using a rotary cheese grater fitted with the finest holes, grate the nuts onto a plate. They should have the light, dry texture of fine meal. Set aside.
2. Reduce the oven temperature to 325 degrees. Butter and flour the bottom and sides of a 9-inch springform pan.
3. Separate the eggs, putting the yolks and whites in separate large mixing bowls. With an electric stand mixer or using a hand-held mixer on medium speed, beat the yolks with half the sugar until pale yellow, thick and fluffy, about 4 minutes. Beat in the lemon zest. Set aside.
4. With clean beaters, beat the whites on low speed with a pinch of salt to break them up, then raise the speed to medium and beat to soft peaks. Increase the speed to high and add the remaining sugar gradually. Continue beating to firm peaks.
5. Pour the beaten egg yolks over the egg whites, sprinkle with one-quarter of the ground walnuts and fold gently. Fold in the remaining walnuts one-quarter at a time, taking care to preserve the volume of the batter and folding just until the nuts are incorporated.
6. Pour the batter into the prepared pan. Bake on the oven's middle rack until the cake is firm to the touch and golden on top and a toothpick comes out clean, 45 to 55 minutes. The cake will puff and rise in the oven but will settle and sink in the center as it cools. Cool in the pan on a rack for 20 minutes, then remove the sides of the pan and continue cooling the cake on the rack. Just before serving, dust the surface with powdered sugar, using a sifter or shaker.