Add eggs to a large mixing bowl and beat. Mix in the sugar and shortening. Stir in the buttermilk and add all-purpose flour, baking powder, baking soda, salt, nutmeg, and cinnamon.
Once the dough is mixed divide it in half. Flour the counter and turn the dough balls onto the surface. Lightly flour the dough before rolling it out to ⅓ inch thick.
Once the dough has been rolled allow it to sit for 20 minutes.
In the meantime, pour oil into a high-sided skillet. Heat it to 370-380°F.
Cut donuts (and holes) out using a donut cutter.
Once the oil is hot, fry one donut to test. Adjust the oil temperature accordingly.
Use a wide spatula to place the donuts in the oil. Place as many as can easily be turned, usually about 3-4. Turn donuts as they rise to the surface. Fry for about 3 minutes until golden all over. Use a long fork to lift out. Be careful they don't get poked or smashed.
Drain on a wire rack and cool on a paper towel.