Beat the egg, ¼ cup vegetable oil, milk, and vanilla extract in a separate bowl.
Slowly stir the wet ingredients into the dry ingredients until well combined.
Gradually add ½ cup all-purpose flour while kneading the dough until it becomes smooth and pliable. (Add up to ¼ more flour if the dough is too sticky to handle.)
Divide the dough into 64 portions and roll each one into a ball about 1 inch in diameter.
Arrange 8 of these balls in a circle to form a ring, then repeat until you have 8 rings.
Heat the remaining vegetable oil to 350 F in a deep, heavy pot. (You may only need 3 cups of oil, depending on the size of the pot.)
Fry the donuts for about 3 to 4 minutes or until they're golden brown and cooked through, working in batches so as not to overcrowd the pan.
Remove the donuts from the oil and drain them on a wire rack over a baking sheet.
Combine the powdered sugar, vanilla, and as much milk as is needed to get the desired consistency.
Sprinkle the donuts with powdered sugar, then drizzle them with glaze.
Eat the donuts alone, with fruit, or enjoy them with coffee.