In a large, heavy-bottomed pot, heat 2-3 inches of oil to 370° F. (I aim for 380° because by the time you add your donuts in, the temperature will drop to the right where you want it at 370°.)
For best results, stir everything by hand! In a large bowl, whisk flour, salt, baking powder, baking soda, spices, and brown sugar together to combine.
Create a well in the center of the dry ingredients. Pour in remaining wet ingredients into the well and whisk together to break apart the eggs.
Begin incorporating all the dry ingredients until a thick dough forms. It might take 2-3 minutes to incorporate all the dry ingredients.
Cover and refrigerate dough for 10-20 minutes.
Flour a board (or clean counter) and flour the dough well. Roll out dough to 1/2-inch thickness. Use a donut cutter to create 3-inch donuts.
Fry 2-3 at a time: brush excess flour off of cut donuts and slide into hot oil gently.
Fry 30 seconds per side (15-20 seconds for donut holes), and drain on paper towels until cool enough to handle. Watch your thermometer as you fry and adjust as you go.
For the glaze- whisk powdered sugar together with vanilla extract, melted butter, and enough milk to create a glaze slightly thinner than white school glue.
Dip warm donuts into glaze and place on a cooling rack to drip and dry. The glaze won't stay white on the donut if you dip them warm, so if you'd like a more obvious glaze, either re-dip them again into the glaze once completely cooled, or wait until they're completely cooled, to begin with.