Preheat oven to 350°F. Spray a 9-inch round OR square baking pan with cooking spray.
Combine rice flour, corn starch, baking soda, baking powder, xanthan gum, pumpkin pie spice and salt in a medium bowl; set aside.
Beat eggs, vanilla, sugar, mayonnaise and pineapple with juice in a large mixer bowl.
Gradually beat in flour mixture until blended. Stir in carrots and nuts. Pour into prepared pan.
Bake for 40 to 45 minutes or until wooden pick inserted in center comes out clean. Cool on wire rack. Frost with cream cheese frosting.
Recipe Note: Recipe may be doubled for a 2-layer (9-inch) cake, as shown in photo OR a 13 x 9-inch cake.
**Xanthan gum is available at larger grocery stores or specialty food stores.