For Cake:Preheat oven to 350 degrees.Whisk eggs. Add oil, applesauce, sugar and vanilla. Mix.Add flour, baking soda, baking powder, cinnamon, ginger, nutmeg, and salt in a separate bowl. Mix to incorporate. Combine egg and flour mixture till mixed. Add in carrots stirring to mix. Grease each wedge thoroughly with melted butter or cooking spray. Pour batter into each wedge filling about 2/3 full. Recipe will make 16 wedges. Once first batch of 8 is removed from oven, let cool for 10 minutes and remove to cooling rack. For second batch, butter wedges with silicone brush. Add batter to fill to 2/3 of wedge. Bake for 18-20 minutes. These are shallow molds so check with cake tester or toothpick to see if cake is done. For Icing:Add butter into mixing bowl. Using KitchenAid stand or hand held mixer, beat till smooth and fluffy. Carefully add in powdered sugar to creamed butter. Blend together. Add in vanilla. Add 1 tablespoon of milk. If mixture is too thick, add more milk to desired consistency. Have two bowls, one for each final color for the cake. One for orange and one for green. You will only need about 1/4 cup of icing for the green portion of the cake. The rest is for the orange portion of the carrot decoration.To create the orange color for the carrot, start with 1 drop of red and 2 of yellow mixing to blend food color. Continue to desired color. You may need to add extra drops of each until you achieve preferred color. For green icing, you will need just a small bowl of green icing for the stem.You can use a frosting decorating bag to pipe the icing or a plastic sandwich bag with the tip cut off as well.
If you prefer a cream cheese frosting instead of icing, that works too!