To prepare cake, peel beets using a vegetable peeler. Grate beets, using the large holes of a grater, to measure 2 cups.
Coat 2 (9-inch) round cake pans with cooking spray; line bottoms with wax paper. Coat wax paper with cooking spray.
Combine the granulated sugar, brown sugar, oil, and eggs in a large bowl; beat with a mixer at medium speed until well-blended. Add beets; beat well. Lightly spoon the flour into dry measuring cups; level with a knife. Combine flour and next 5 ingredients (flour through salt) in a large bowl, stirring well with a whisk. Add flour mixture to sugar mixture alternately with milk, beginning and ending with flour mixture. Pour batter into prepared pans; sharply tap pans once on counter to remove air bubbles.
Bake at 350° for 30 minutes or until a wooden pick inserted in center comes out clean. Cool in pans 10 minutes on wire racks; remove from pans. Carefully peel off wax paper, and cool cake completely on wire racks.
To prepare frosting, beat orange rind, vanilla, and cream cheese with a mixer at high speed until fluffy. Add the powdered sugar; beat at low speed just until blended (do not overbeat).
Place 1 cake layer on a plate; spread with 1/2 cup frosting; top with remaining cake layer. Spread remaining frosting over top and sides of cake. Sprinkle nuts over top of cake. Store cake loosely covered in refrigerator.