Preheat oven to 350 F. Grease a muffin pan or spray paper liners to prevent sticking and set aside. In a medium bowl, mix flour, baking powder, soda, sugar, salt & cinnamon in a medium bowl. In a large bowl, mix applesauce, vanilla and carrots. Add dry mix to wet mix in 3-4 batches. Stir until just combined. Fill cups to the top bake 15-25 minutes or until a toothpick inserted in the center comes out clean.
For cream cheese icing, use electric beaters to whip and combine 1 container Tofutti cream cheese, 1 tsp vanilla extract and 1/2 cup confectioners sugar at a time until the consistency is thick and sweet enough.
For maple icing, use electric beaters to whip and combine 1 cups confectioners sugar, 3 tbsp maple syrup and 1 tsp cinnamon, adding additional sugar as necessary to reach a thick and fluffy consistency.