Line a large baking tray with parchment paper and set aside.

Mix the flour, sugar, yeast, and salt together in a stand mixer fitted with a dough hook.

In a measuring jug, heat the milk and water until lukewarm. Stir in the melted butter and vanilla extract.

Turn the mixer on low speed and slowly add the milk mixture. Mix for 2 minutes to wake up the yeast. Use a spatula to ensure everything is mixed well.

Increase the speed to medium and mix until the dough is shiny and smooth, 6-8 minutes. The dough should be saggy and on the wetter side.

Rub the mixing bowl with a little oil and place the dough in the bowl, turning to coat lightly.

Cover the bowl with plastic wrap and a kitchen towel, allowing the dough to proof at room temperature until doubled, 1 ? - 2 hours.

On a floured surface, roll out the dough to ?-inch thick.

Using a round 3-inch cutter, cut out as many donuts as possible. Cut out the donut holes with a smaller cutter. If making stuffed donuts, do not cut out a hole. Re-roll scraps to yield more donuts.

Cover the donuts with cling film and let them rise at room temperature for 20-30 minutes.

Preheat the oven to 350?F (180?C).

Brush the tops (not the sides) of the donuts with melted butter. Sprinkle 2 tablespoons of water on the tray to create steam while baking.

Bake for about 13 minutes, or until lightly browned.

Take the donuts straight from the oven and dip each in the bowl of vanilla glaze one at a time. Let the excess glaze drip off before placing them on a wire rack to set. Add sprinkles if desired.

For pumpkin pie spice donut holes, mix the sugar, pumpkin pie spice, and salt in a small bowl. Toss the holes in melted butter, then coat in the sugar spice mix. Serve with chocolate sauce.

For stuffed donuts, fit a piping bag with a medium nozzle and fill with Nutella, jelly, or pastry cream. Poke a hole in the bottom or side of each donut and fill. Swirl on top to indicate the filling.