Preheat oven to 350 degrees F. Grease donut pans and set aside.
In a large bowl, whisk together the flour, baking powder, baking soda, spices, and salt.
1 cup all-purpose flour, 1/2 tsp baking powder, 1/2 tsp baking soda, 1 tsp cinnamon, 1/4 tsp ground ginger, 1/4 tsp salt
In a separate bowl, whisk eggs with sugar until pale. Add oil, Greek yogurt, and vanilla.
1/2 cup sugar, 1 egg, 2 tbsp oil, 1/2 cup Greek yogurt, 1 tsp vanilla
Add half of the flour mixture to wet ingredients. Stir in grated carrots. Add remaining flour and mix until just combined.
1/2 pound carrots
Spoon batter evenly into prepared donut pans and bake for 15 minutes, or until a toothpick inserted into the center of a donut comes out clean.
Once baked, allow to cool slightly before inverting onto a cooling rack. Cool completely before frosting.
To make the frosting, beat cream cheese and butter on medium high speed with a hand mixer for 2-3 minutes. Add powdered sugar and beat until light and fluffy.
4 oz cream cheese, 1/4 cup butter, 1 cup powdered sugar
Use an offset spatula to frost cooled donuts and sprinkle with toasted coconut, if desired.
1/4 cup toasted coconut flakes for topping