Preheat the oven to 180 C. Grease the doughnut tray with melted butter.
Into a large bowl, sift in flour, sugar, baking powder, ground cinnamon and ground nutmeg.
In a another bowl, whisk together milk, eggs and butter. Pour this mixture into the dry ingredients. Using a spatula or wooden spoon, gently fold the batter to combine.
Spoon the batter into the prepared baking tray. Bake for 15-17 minutes or until a toothpick inserted comes out clean. Transfer the doughnuts onto a wire rack.
Combine sugar and cinnamon in bowl and set it aside. Melt 3 tbsp of butter. Dip each doughnut in the melted butter and then in the cinnamon sugar mix. Shake off the excess and place on the serving plate to enjoy!