Add oil to a 10-inch skillet (or skillet of a similar size) so that you have about an inch of oil. Heat over medium-low heat to 360 degrees.
While oil is heating, make doughnut batter. In a large bowl, whisk together flour, sugar, baking powder, and salt.
In a separate, smaller bowl, whisk together buttermilk, egg, melted butter, and vanilla.
Pour the liquid ingredients into the dry ingredients and mix together until just combined, taking care not to over-mix. Fold in ¼ cup nonpareils.
When oil reaches 360 degrees, drop small balls of dough into the oil (using about 1 tsp of dough- doughnuts will increase in size once fried), working in batches and making sure not to overcrowd the skillet. Let each doughnut fry for about 1 ½ minutes on one side before flipping over with tongs and frying another minute.
Remove doughnut holes from oil and place on paper towel-lined baking sheet. Monitor oil to make sure it remains at about 360 degrees. Continue frying with remaining dough. Let doughnut holes cool completely.
Place remaining cup of nonpareils in small bowl.
Once doughnut holes are cooled, brush glaze on with a pastry brush (you can also dunk doughnut holes into icing; just make sure to let excess drip off). Roll doughnut holes in nonpareils. Set on a piece of waxed or parchment paper to let icing dry.