In a mixing bowl, combine the active sourdough starter, all-purpose flour, granulated sugar, and salt. Use a whisk to ensure these dry ingredients are blended evenly.

In a separate container, whisk together the whole milk, large egg, and melted unsalted butter until well mixed.

Gradually pour the wet mixture into the dry ingredients while stirring with a spatula. Mix until the dough starts to come together.

Once combined, knead the dough gently in the bowl for about a minute until it becomes a cohesive ball.

Cover the bowl with a clean kitchen towel or plastic wrap, and let it rest in a warm spot for about an hour.

After the dough has risen, turn it out onto a lightly floured surface. Roll it out to about ½-inch thickness with a rolling pin.

Use a biscuit cutter or round cookie cutter to cut out donuts, dipping the cutter in flour between cuts.

Heat the neutral cooking oil in a deep frying pot or pan over medium heat.

Fry the donuts in batches, turning them to ensure even cooking until golden brown.

Remove the cooked donuts with a slotted spoon and transfer them to a cooling rack.

For the glaze, mix powdered sugar, whole milk, and vanilla extract in a bowl until smooth.

Once the donuts are cool enough to handle, dip the tops into the glaze, allowing any excess to drip off.