2/3 cup shortening
2/3 cup sugar
1 egg
1 cup grated carrots (I have used freshly grated or cooked and mashed and can't tell a difference)
1 tsp vanilla
2 cups flour
2 tsp baking powder
1/2 tsp salt

Cream shortening and sugar. Add egg, vanilla, and carrots. Then add dry ingredients. Dough will be stiff (add a little milk if too stiff). Bake at 350 for 15 minutes. Then frost with the following glaze:
Mix 3/4 cup powdered sugar, 1 tbsp melted butter, and 1/4 tsp grated orange ring. Add enough orange juice to desired consistency.