Fill a pot with about 3 inches of vegetable or canola oil and heat over medium high heat to 375 degrees.
While the oil is heating, add the butter and sugar to a stand mixer fitted with the dough hook and beat together until combined.
Beat in the egg until just combined.
In a separate bowl, stir together the flour, baking powder, baking soda, nutmeg, cinnamon, and salt.
Alternate adding the buttermilk and flour mixture to the sugar until everything is well combined. Knead for just a couple of minutes. If the dough is too sticky to roll out, add more flour until it's workable, a tablespoon at a time, being careful not to add more flour than is needed.
Dump the dough out on a floured surface and pat flat. Sprinkle the dough with half of the blueberries and fold dough over on itself. Flatten and sprinkle with remaining blueberries. Fold dough over to cover blueberries and roll out to 1/3 inch thick. Use a donut cutter to cut donuts. Reroll the dough as needed.
Add a few donuts at a time to the hot oil, being careful not to overcrowd the pan. Fry until golden, about 2 minutes each side. Fry the donut holes as well, about 1 minute.
Remove the donuts to a paper towel lined plate and let the grease drain off.