In a large mixing bowl use a whisk to sift together the flour, sugar, baking powder, salt, cinnamon and ground nutmeg.
In a separate bowl, whisk together the buttermilk, shortening, vanilla extract and egg until well combined.
Pour the wet ingredients into the dry ingredients and stir until just combined, being careful not to overmix. The dough should be soft and slightly sticky.
Turn the dough out onto a well floured surface and turn to coat with just enough flour that it's not tacky. Roll it out to 1/2-inch thickness.
Use a donut cutter or a 3-inch biscuit cutter to cut the dough into rounds. If using a biscuit cutter, use a 1-inch cutter for the centers. Gather any scraps, reroll and cut out more doughnuts until all of the dough is used.
Fry: On the stovetop, heat oil in a deep fryer or 6 quart Dutch oven or pot to 365°F-375°F. Carefully add the doughnuts to the hot oil frying 2-3 at a time to avoid overcrowding the pan. Don't walk away.
Fry the doughnuts in batches for 1 1/2 - 2 minutes on each side or until they are golden brown and cooked through. Remove the doughnuts from the oil using a stainless steel spider or slotted spoon and place them on a paper towel-lined sheet pan to drain excess oil.
Glaze: In a medium bowl whisk together butter, milk, vanilla and almond extract. Add powdered sugar 1/2 cup at a time. Whisk until smooth adding more milk as needed to thin.
Dip the warm doughnuts into the glaze placing them onto a sheet pan fitted with a wire rack without touching. Double dip for a heavier glaze, if desired. (Optionally, you can dust them with powdered sugar.)
Enjoy warm!