Preheat oven to 425°F. Prepare doughnut pan with vegetable pan spray.
In large bowl whisk together flour, sugar, baking powder, cinnamon, salt and nutmeg.
In medium bowl, whisk together buttermilk, eggs, and melted butter. Add buttermilk mixture to flour mixture, mixing just until incorporated. Fold in carrots and walnuts. Divide batter evenly into prepared pans.
Bake 9-11 minutes or until doughnuts spring back when lightly touched. Cool 5 minutes in pan, then remove to cooling grid to cool completely.
For glaze, in microwave-safe bowl, microwave cream cheese at 50% power in 30 second intervals until cream cheese is slightly melted. Add confectioners’ sugar and milk; whisk until smooth. Top doughnuts with glaze and walnuts, if using.