Preheat oven to 350F degrees and adjust the oven rack to the middle position. Spray each donut cup with non-stick cooking spray and set aside.
In a medium bowl, whisk together the flour, baking powder, salt, and spices.
In a small mixing bowl or large liquid measuring cup, add the sugar, orange juice, zest, milk, egg, vanilla extract. Whisk to combine thoroughly. Add the wet ingredients and the melted butter to the dry ingredients. Use a spatula to fold the batter until no dry streaks remain. Add the grated carrots and fold until just incorporated.
Spoon equal amounts of the batter into the donut wells, and smooth the batter with the back of the spoon. You can also transfer the batter to a piping bag and pipe into the donut wells.
Bake for 14 - 16 minutes, or until the tops of the donuts spring back when lightly poked with your finger. Cool the donuts in the pan set on a wire cooling rack for 5 minutes then transfer to the wire rack to cool completely.
Once the donuts are completely cool, glaze the donuts. Either dip the donuts into the glaze, or smooth it on with an offset spatula. The donuts are best enjoyed the day they are baked. Enjoy!