To begin, pour 2-3 inches of vegetable oil into a Dutch oven or heavy pot. Start heating the oil. This will take a while, so you can prepare the dough while it is heating. Your target temperature is 375 degrees (F).
In your mixing bowl, beat together the sugar, shortening, and eggs. Add in 2 cups of the self-rising flour, the cinnamon, and nutmeg. Mix well. Pour in the milk and mix again. Add in another 1 1/2 cups of self-rising flour. Mix until smooth.
Turn the dough out onto a well floured surface. With floured hands, knead the dough, adding additional flour as needed until you have a soft, yet manageable dough. Pat the dough out to 3/4 inch thick.
About now, your oil should be heated. You will need to monitor this closely and adjust the stove as needed to keep the temperature steadily at 375 (F). IF the oil gets too hot, the doughnuts will cook too quickly and be browned before they are cooked all the way through. If the oil is too cool, it will soak into the doughnuts and they will be greasy. Neither of those would be very appealing. The oil temperature can vary between 370-380, but don’t let it get outside of that range. Again, shoot for 375.
Cut the dough with a floured doughnut cutter. (If you don’t have a doughnut cutter, you can use a biscuit cutter or a glass. Simply poke your finger through the middle to make a hole in the center.)
Cut 3 or 4 at a time. With a wide spatula, slide the doughnuts and holes into the hot oil. Cook them for about a minute and a half on each side, until they are golden.
As they finish cooking, transfer them to a platter that is lined with several layers of paper towels. Repeat with the remaining dough.
Serve the doughnuts plain or shake them, one at a time, in a paper bag with granulated or powdered sugar. You could also coat them with a glaze. Store the doughnuts in an airtight container. They will keep for about 48 hours. Enjoy!