In a bowl, combine flour, salt, baking powder, baking soda, and nutmeg.
In the bowl of a stand mixer, beat together the eggs, buttermilk, granulated sugar, and brown sugar until well combined. Add the flour mixture and beat until just combined. Next, add the vanilla and shortening and mix until just combined.
Put the dough on a well-floured surface. Knead until it comes together. (The dough is very sticky so you may need a lot of flour). Using a rolling pin, roll the dough out until it is about a 1/2 in thick. Next, cut out the doughnuts. During this, you can cut out holes in the center or leave the doughnut as is.
Put the doughnuts on a well-floured baking sheet a refrigerate for 30 minutes to an hour.
Heat the oil until it reaches 360 degrees Fahrenheit. Fry the doughnuts, 3-4 at a time depending on the size of your pan, for 1-2 minutes on each side. DO NOT OVERCROWD. This will decrease the temperature of the oil and thus mess up the frying process.
Once doughnuts are cooked (cut the first one to check), transfer them to a cooling rack on a baking sheet (this will prevent the oil from making a mess on your counter).
To make the glaze, combine the 4 ingredients in a mixing bowl. Do not worry if there's blueberry chunks. They will not stick to your doughnut unless you want them to!
Once the doughnuts have cooled for at least 5 minutes, dip in the glaze, serve, and enjoy!