Preheat the oven to 350°F. Make sure to spray the donut tray, or rub butter around the edges so that the dough doesn't stick to the pan
In a large mixing bowl, mix together the try ingredients. Flour, baking powder, salt, cinnamon, ginger, and all spice. Set the bowl aside
In a separate mixing bowl, mix together the butter, buttermilk, brown sugar, egg, and vanilla until fully combined.
Add the dry ingredients to the wet ingredients and mix until just combined. Add the grated carrots and gently mix them into the batter.
Spoon the batter into each cavity of the donut. I used a piping bag because it was easier to place the dough in the pans neatly.
Bake for about 10 minutes at 350°F or until a wooden toothpick inserted into the donut comes out clean. Remove from the oven and cool in the pan for about 5 minutes. Remove the donuts from the pan and transfer to a wire rack to finish cooling.
In a mixing bowl, using an electric mixer, beat the cream cheese, powdered sugar, and milk.
Frost the cooled donuts and decorate as desired.