Fill a frying pan halfway with oil. Heat over medium heat until the oil reaches 375°F with a candy thermometer.
Make the glaze by combining the sugar, vanilla, and 3 teaspoons of water. Add more water, 1 teaspoon at a time, until a pourable consistency is reached.
Separate the dough into 8 biscuits.
Cut each biscuit into 4 pieces, pinching the edges to keep the dough from spreading (fanning out) during the cooking.
Drop the dough into the hot oil and cook until brown. Flip the donuts with a metal slotted spoon to cook the other side.
Place the cooked dough on a paper towel to absorb the grease, and then drop the donuts into the bowl of glaze and turn to coat evenly.
Place on a wire rack to cool slightly.