Preheat the oven to 350 F/180 C. Lightly butter or spray two donut pans and set them aside.
In a large mixing bowl, whisk together the buttermilk, melted butter, brown sugar, egg, finely grated carrots, sour cream, olive oil, and vanilla extract until combined.
Then mix in the flour, baking powder, baking soda, salt, cinnamon, ginger, nutmeg, clove, and finely chopped pecans until just combined.
Fill a piping bag or ziplock bag with the carrot cake batter and cut the tip.
Pipe the batter into the greased donut pan about ¾ full. You will have enough batter to make 10 donuts.
Bake the donuts in the preheated oven for 10-11 minutes, or until the tops spring back when touched.
Let them cool on a wire rack for 10 minutes, then gently remove them from the pan.
Make sure they are completely cool before frosting! You can decorate them with cream cheese carrots, candied pecans, or half and half like I did!