Place all the ingredients into a bowl and mix until well blended and smooth.
Mix the flour, sugar, salt and baking powder together, sift and set it aside.
In a smaller bowl, whisk the egg, milk and vanilla extract.
Before you mix the wet ingredients into the dry ingredients, pour the oil into a heavy saucepan. Place it over medium heat and use a thermometer to heat to 350 degrees. Keeping the oil at 350 degrees will cook the donut holes perfectly. If you heat gets too hot, it will burn the oil and make the donuts taste bad so watch the thermometer closely.
Pour the egg mixture into the flour mixture and mix until well combined.
Once the dough is mixed, add the melted butter and mix until combined. Once the oil reaches 350 degrees, drop little dough balls into the hot oil. If the dough is not round when you drop it in the oil, the donuts won’t be round. If you use a small cookie scoop it will help them have a round shape. If you don’t have a cookie scoop they may not be rounded unless you roll them into a ball in your hands.
Don’t put too many in the pot at one time because they need room to float around.
When they start turning brown on the underside, use a fork to flip them over. Continue to cook until they are nice and golden brown.
Remove them with a slotted spoon and place them on a plate lined with a paper towel.
Allow them to cool for a few minutes and then dip them one at a time into the glaze.
Place them on a rack with a piece of wax paper under it to catch the excess glaze as it drips off the donuts.