Preheat the oven to 425 degrees F and lightly grease your donut pans. Set aside.
In a large bowl, stir together butter and oil. Add sugar and whisk until combined.
Add milk, eggs, vanilla and whisk until combined. Stir in carrots.
Add flour, baking powder, cinnamon, salt, baking soda and nutmeg and stir just until combined.
Spoon or pipe batter into prepared pans, about 3/4 full.
Bake for 7-8 minutes, until a toothpick inserted in the center comes out clean. Let cool for 5 minutes before removing to a wire rack to cool completely.
Cream Cheese Frosting:
In a large bowl, beat together cream cheese, butter, and vanilla until smooth. Add powdered sugar and beat until smooth — this might take 4-5 minutes but it will come together!
Spread on cooled donuts and decorate as desired (I used toasted coconut!). Serve.
Leftovers may be stored in the refrigerator up to 3 days or in the freezer up to 3 months