1Heat oven to 350°F. Grease bottom only of 8- or 9-inch square pan with shortening, or spray with cooking spray.
2In large bowl, beat cake mix, water, 1/2 cup butter, cinnamon, nutmeg, 2 teaspoons vanilla and eggs on low speed 30 seconds. Beat on medium speed 2 minutes, scraping bowl occasionally. With spoon, stir in carrots and pecans. Spread in pan.
3Bake 36 to 41 minutes for 8-inch pan or 33 to 38 minutes for 9-inch pan or until toothpick comes out clean. Cool completely, about 1 hour.
4In large bowl, beat cream cheese, 2 tablespoons butter, 1/2 teaspoon vanilla and 1 teaspoon milk with electric mixer on low speed until smooth. Gradually beat in powdered sugar, 1 cup at a time, until smooth and spreadable. If frosting is too thick, beat in more milk, a few drops at a time. Stir in coconut. Spread frosting over cake.