In a small mixing bowl, mix the flour, baking powder, cinnamon, and nutmeg, if using.
Add the sugar and eggs to the bowl of a stand mixer fitted with the paddle attachment. Beat on medium-high speed until the mixture is smooth and pale yellow.
Next, add the melted butter and buttermilk and mix just until combined.
Switch to the dough hook attachment and add the dry ingredients to the bowl. Mix on low speed until a smooth dough forms-- about 2-3 minutes.
Place the dough in a lightly greased bowl and place it in the fridge to chill for at least one hour.
After the dough has chilled, heat 3-4 inches of neutral oil into a large dutch oven and bring its temperature up to 375F.
While bringing up the oil temperature, roll out the dough to 1/2” thickness on a well-floured surface.
Using a 2 1/2” floured round cutter, cut out the doughnuts. Score the top of the doughnuts with a sharp knife.
Carefully place a few doughnuts at a time into the oil and fry until golden brown-- about 2 minutes per side. Make sure not to crowd the pan too much.
Carefully remove the doughnuts from the oil and place them on a paper towel to remove excess oil, then transfer them to a wire rack to cool slightly.