Pour vegetable oil into heavy bottomed pot (or fryer). Heat until 350 degrees is reached.
Line a baking sheet with paper towels and if available place a cooling rack on top to allow oil and glaze to drip off.
In one bowl mix together the dry ingredients: flour, sugar, baking powder, and salt. In another bowl whisk the milk and egg together. Add the wet ingredients into the dry. Then add the butter until a soft yet thick dough forms.
Using a cookie scoop or spoon scoop dough into a ball and drop in fryer* in batches. You do not want to overcrowd.
Fry the donut holes for 2 minutes on one side until deep golden brown and an then use a pair of tongs to flip and fry an additional minute. (Fry a little less if making smaller donut holes).
Using a slotted spoon remove the donut holes to the prepared baking sheet.
Repeat with any additional dough.
Then one by one dip the donut holes into the glaze** and return back to the rack. Serve warm.