Preheat oven to 350°F. Grease a donut pan with nonstick spray. Set aside.
In a medium bowl, whisk together flour, cinnamon, baking powder, baking soda, ginger, salt, nutmeg, and cloves. Set aside.
In a large bowl, use a hand mixer to beat together egg and brown sugar until combined and caramel in color. Add milk, oil, and vanilla and stir to combine.
Add bowl of dry ingredients to bowl of wet ingredients and stir until just combined. Add grated carrots and stir until thoroughly combined.
Pour the batter into the prepared pan, filling each ⅔ full. The easiest way to fill them is to use a pastry bag (or a plastic bag with a hole cut into the corner). Bake for 13-15 minutes (14 minutes is perfect for me), until set and golden. Let set in pan for a minute or two, and then remove from pan and let cool completely on wire racks.