3 1/2 C flour
1 C sugar
1/2 tsp baking soda
2 tsp baking powder
1 tsp salt
1 1/2 tsp nutmeg
3/4 C buttermilk
4 Tbsp unsalted butter, melted
2 large eggs
1 large egg yolk
6 C vegetable shortening for frying (or use a deep fryer)
3 C powdered sugar
1/2 tsp salt
1/2 tsp vanilla extract
1/2 C cold water
Mix 1 C flour, sugar, baking soda, baking powder, salt, and nutmeg, in a large bowl.
Mix butter, buttermilk, and eggs, in a separate bowl. Combine wet ingredients with dry and beat until smooth. Decrease mixer speed to low. Add remaining flour. Mix until just combined. The consistency should be somewhere between cookie dough and cake batter.
Heat oil fryer to 375 F degrees.
Turn dough out onto a floured work surface. Roll with a heavily floured rolling pin until dough is about 1/2" thick. Stamp out dough rings with a donut cutter (or use two circle cutters, with the second being about half the diameter of the larger one). Transfer rounds to a large wire rack. Gather the scraps, remix, and repeat rolling and stamping until all the dough is used.
Carefully lower dough rings into hot oil, four or five at a time. Use tongs to turn donuts as they rise to the surface. Fry donuts until golden brown, about 50 seconds per side. Drain on a paper towel-lined wire rack (brown paper bags work better, if you have any). Repeat until all the donuts are cooked.
For the glaze:
Place wire rack over a baking pan, to collect glaze drippings. Mix all glaze ingredients in a mixing bowl, until completely smooth.
Dip cooked, but mostly cooled, donuts into glaze until half submerged. Remove from glaze and return to wire rack.
Second dip in glaze for a thicker coating (optional).