Pour enough oil into a large pot to give you about an inch to two inches of oil. Heat oil to 365°F, over medium-high heat. Use a frying thermometer or a candy thermometer to ensure proper temperature. While oil is heating prepare donuts, (keep an eye on the oil temperature).
In a medium bowl, whisk together flour, ½ cup sugar, baking powder, cinnamon, nutmeg, and salt.
In a separate bowl, whisk together buttermilk, vanilla, rum extract, and melted butter.
Add the buttermilk mixture to the flour mixture, and using a fork, mix just until combined. Do not over mix.
On a lightly floured surface, roll dough to ½-inch thickness with a floured rolling pin. Then use a 3-inch pastry cutter and a 1-inch pastry cutter, cut out donuts and donut holes, placing cut-donuts on a parchment paper-lined baking sheet or cutting board. Re-roll as needed to use all the dough.
Once your oil has reached 365°F, place no more than 3 donuts in the oil at a time (or you run the risk of cooling your oil too much). Fry for about 2 minutes, flipping once. Donuts are done when they are golden-brown on both sides. Move to a paper towel-lined cooling rack to cool. **Keep an eye on your oil temperature and adjust the heat up or down to maintain a temperature of 355°F to 365°F.**
Allow fried donuts to cool to room temperature before dipping them in frosting.