Heat oven to 350°F. Grease bottom and sides of one 13x9-inch pan or two 8-inch or 9-inch round pans with shortening; lightly flour.
In a large bowl, beat granulated sugar, oil, and eggs with an electric mixer at a low speed about 30 seconds or until blended. Add flour, cinnamon, baking soda, 1 teaspoon vanilla, and the salt; beat on low speed for 1 minute. Stir in carrots and nuts. Pour into pan(s).
Bake 13x9-inch pan 40 to 45 minutes, round pans 30 to 35 minutes, or until a toothpick inserted in center comes out clean. Cool rectangle in pan on a cooling rack. Cool rounds 10 minutes; remove from pans to cooling rack. Cool completely, about 1 hour.
Frost 13x9-inch cake or fill and frost round layers with frosting. Sprinkle nutmeg on frosted cake and top with additional chopped nuts, if desired. Store in refrigerator.
Substitute a gluten-free flour mix for the all-purpose flour.