Preheat the oven to 350 degrees F (175 degrees C). Line a 12-cup muffin tin with paper liners.

Place carrots in a saucepan with water to cover. Bring to a boil, reduce heat, and cover. Simmer until carrots are soft, 7 to 10 minutes. Drain well and transfer to a blender. Add grated ginger and puree until very smooth. Drain out the juices.

Combine sugar and butter together in a large bowl. Add egg whites, 1 at a time, mixing well after each addition. Stir in applesauce and vanilla extract. Stir in pureed carrot-ginger mixture. Add oat flour, baking powder, cinnamon, baking soda, and allspice. Stir until just combined, but do not overmix. Fold in raisins, pineapple, coconut, and walnuts.

Fill each muffin cup 3/4 full with batter.

Bake in the preheated oven until a toothpick inserted in the center of a muffin comes out clean, 12 to 14 minutes.