These are baked, using a donut pan.
Preheat oven to 350 degrees (F).
Beat the egg in a large bowl. Beat in the juice, butter, orange zest, and sugar.
Add the flour, baking powder, baking soda, and spices. Mix until blended.
Stir in the grated carrots.
Spoon the mixture into donut pan, filling each ring.
Bake for 9 - 11 minutes. Place on a wire rack and cool completely.
Cream the butter and cream cheese together until fluffy.
Stir in the orange zest and orange juice.
Beat in 1 cup sugar. Beat in more sugar, a tablespoon at a time, until the frosting holds it's shape.
Stir in the orange food coloring, if using, until desired shade is reached.
Spread the frosting on the cooled donuts.
Decorate with sprinkles or orange zest if desired.