Dissolve yeast in luke-warm water. Set aside.
Heat milk in the microwave for 2-3 minutes.
While milk is heating, add shortening to a large bowl. Pour hot milk over it and whisk until mixed (there will still be a few shortening clumps). Add salt, sugar, nutmeg, and cinnamon. Mix well with a wooden spoon. Add 4 eggs and mix well.
Add salt, sugar, nutmeg, and cinnamon and mix well with a wooden spoon. Add eggs and continue to mix, followed by the yeast mixture.
Add 2 cups of flour and mix with a wooden spoon. Continue to add flour (1-2 cups at a time) until the batter is no longer runny and is smooth. NOTE: you can also use a stand mixer.
Sprinkle flour onto a clean surface and place dough onto it. Gently knead dough until the surface is not sticky to the touch. NOTE: The dough should be very soft but not so sticky that you can't handle it fairly easily. Place the soft dough into a lightly greased bowl. Cover the bowl and let rise for 1 to 1½ hours. The dough should be about double in size when it's ready.
Place dough on a lightly floured surface and roll out to a 1 inch thickness. Cut the donuts out as closely as possible (save the middles for doughnut holes). Move donuts and holes to a clean surface. Cover and let rise for 1 to 1½ hours.
Mix glaze by mixing ingredients together in a large bowl.
Once the donuts and holes are done rising, fry them in a large frying pan with vegetable oil until golden brown (temperature of the oil should be between 365-380°F).
Add hot donuts to glaze making sure both sides are coated. Place on a wire rack over parchment paper to let excess glaze drain.