Heat the oil in a large, heavy pot or Dutch oven to 375ºF.

While the oil is heating, make the donuts: place the sugar and shortening into a bowl and beat with a hand mixer until it is combined. Add the egg and the vanilla and continue to beat until combined.

In another bowl, whisk together the flour, baking soda, salt and nutmeg.

Add 1/3 of the flour mixture to the sugar mixture and beat to combine. Add half of the buttermilk, beat, then another 1/3 of the flour. Finish it off by adding the last of the buttermilk, beating to combine, then the remaining flour. Beat just until combined, do not over-beat.

Flour a counter or work surface, then pour the dough out onto it. If the dough is super sticky, knead it a few times in the flour. Roll the dough out to about 1/3” thickness. Use a round cookie cutter to cut out 9 donuts. Use a smaller circle to cut out the centers, then cut more small holes from the scraps.

In another bowl, whisk together the melted butter, the vanilla extract and the almond extract. Slowly start adding the powdered sugar, 1/2 cup at a time, adding in milk as needed. Once all of the powdered sugar has been added, continue adding milk until you have a good glaze consistency.

When the oil is hot, add in half of the donuts. Fry until they are golden brown, then flip and cook the second side. It should take about 3-4 minutes per batch. 

Drain the donuts on a paper towel lined plate. When cool enough to touch, dip both sides in the glaze then transfer to a baking rack to dry.

Repeat with the remaining donuts.