In a stand mixer, combine flour, sugar, salt, milk, baking powder, egg, vanilla, cinnamon, nutmeg, and butter, mixing after each addition. Mix well until a batter is formed.
Fold in the blueberries.
Spray a doughnut pan with non-stick cooking spray. Divide the batter among the wells, filling each one about 3/4 full.
Bake in the oven for 10-15 minutes, or until nicely browned.
While the doughnuts are baking, whisk together powdered sugar, vanilla, and skim milk.
Remove the doughnuts from the oven and let them cool for about 5 minutes, then carefully remove from the pan.