Combine the Dry Ingredients: Mix the all-purpose flour, granulated sugar, active dried yeast, and salt in the bowl of a stand mixer fitted with a dough hook.
Warm the Milk Mixture: Heat the whole milk and butter together in a measuring jug until the butter has melted. Stir in the vanilla extract.
Form the Dough: Set the mixer to low speed and gradually pour in the warm milk mixture. Continue mixing until the ingredients come together into a ball.If the dough appears a little dry, add a small splash of milk. Develop the Dough: Increase the mixer to medium speed and continue mixing for 6–8 minutes, until the dough becomes shiny and smooth.The finished dough should remain somewhat saggy. Prepare the Bowl: Lightly rub a clean mixing bowl with vegetable oil or another flavorless oil.
Begin the First Rise: Transfer the dough to the oiled bowl, turning it once so the surface is lightly coated. Cover the bowl tightly with plastic wrap and let the dough rise at room temperature until doubled in size, roughly 2 hours. Roll the Dough: Turn the risen dough onto a floured work surface. Gently roll it out to approximately ½ inch thick. Cut the Donuts: Use a floured 3-inch round cutter to cut the donut shapes from the dough. Use a much smaller cutter to remove the centers, creating the donut holes. Gather any remaining dough, re-roll it, and continue cutting until finished. The recipe yields approximately 12–14 donuts at this stage. Optional Overnight Preparation: If preparing the donuts ahead, refrigerate the cut donuts until the following day. Before frying, bring them to room temperature and allow them to rise slightly for roughly 30 minutes. Complete the Second Rise: Cover the shaped donuts with cling film and let them rise at room temperature for 20–30 minutes.
Heat the Frying Oil: Pour approximately 2–3 inches of vegetable oil into a medium, deep pan. Heat the oil over medium-high heat for a few minutes.If using a thermometer, bring the oil to 350°F (180°C). Fry the Donuts: Carefully place 3–4 donuts at a time into the hot oil. Fry for about 2–3 minutes, until lightly browned on one side, then turn them over and continue frying until the second side is browned. Drain the Donuts: Remove the fried donuts from the oil and place them on kitchen paper to absorb excess oil. Continue frying the remaining donuts in batches. Glaze While Warm: Dip the freshly fried, warm donuts one at a time into the chocolate glaze. Allow excess glaze to drip off before transferring each donut to a wire rack. Finish with Sprinkles: Add sprinkles over the chocolate glaze while it is still suitable for topping.
Let the Glaze Set: Allow the glaze to dry on the wire rack, then enjoy the donuts as fresh as possible for the best texture and flavor.