Apple Spice Cake

Heat oven to 350°.

Combine cake flour, all-purpose flour, 1/2 cup walnuts, the baking soda, salt, cinnamon and cardamom and dry food processor container fitted with metal blade; processed mixture until nuts are finely ground, about 40 seconds. Transfer the waxed paper.

Shred apples in food processor with shredding disc; transferred to waxed paper. Remove the lemon zest with vegetable peeler; reserve lemon for other use. Combine zest and 1/4 cup of granulated sugar in dry food processor container fitted with metal blade; process until zest is finely minced, about 40 seconds.

Add eggs to sugar mixture. Process, adding hot butter in thin stream within 15 seconds; process 15 seconds. Add remaining granulated sugar; process 22nd. Scrape down side of container. Add apples and vanilla. Process with 2 one–second on/off turns. Add flour mixture; process with 6 or 7 half-second on/off turns just until the flour is mixed into batter. Scrape down side of container.

Pour batter into well buttered 8-inch springform pan. Bake on center oven rack until wooden pick inserted in center is withdrawn clean, 50 to 60 minutes. Cool on wire rack to room temperature. Remove side of pan. Decorate top with powdered sugar and walnut pieces before serving.