Warm the milk to lukewarm and add the yeast and one tablespoon of sugar. Stir and let it sit for 5-10 minutes, it should start to foam up. If you are using instant yeast, you can skip this step.
In the bowl of a stand mixer with a dough hook attachment, add the remaining sugar, eggs, and salt. Once the yeast has activated, add the milk/yeast mixture to this bowl and mix everything to combine.
Add the flour to the mixing bowl and turn the mixer on low for one minute to let the flour mix in.
After a minute, slowly drizzle in the melted butter while still mixing on low speed.
Turn the mixer up to high speed and let it mix for 3-5 minutes or until the dough is no longer sticking to the sides of the bowl. If it seems too sticky, add an extra tablespoon of flour.
Tip your dough out onto a floured work surface and knead by hand until it is no longer sticking to your hands.
Form a smooth ball with the dough and place it into an oiled bowl. Cover with plastic wrap and let proof on the counter until it doubles in size (about 1-2 hours, depending on temperature).
Once the dough has doubled in size, check if it's ready by pressing it lightly with your finger. If it springs back immediately, it needs longer. Once it is ready, it will spring back slowly, and only about halfway.
Punch the dough to knock the air out of it, then tip it onto a floured work surface. Roll it out to ½ inch thick.
Cut rounds out of the dough with a cookie cutter that is 21/2 - 3 inches wide. Place the donuts on a lined cookie sheet with a little space between them.
Cover the tray of donuts loosely with plastic wrap or a kitchen towel and let them proof for another 45 minutes.
Fry the Donuts
In the last 10 minutes of the 45-minute proof, you can start to prepare your frying oil. Pour at least 2 inches of oil into your saucepan and heat to about 350°F / 180°C.
Gently place your donuts into the oil*, and they should start bubbling at the sides. I like to do only 2 or 3 at a time, depending on the size of the saucepan. They fry super fast and this allows you to have more control.
Allow the donuts to bob around and fry for a minute or two, checking the underside from time to time. Once the underside looks golden brown, flip the donut and fry the other side until the color matches. As there are so many variables (oil temperature, donut size, etc), it is impossible to give you an exact time to fry the donuts for - you really have to do it by eye and see when they look ready.
Once both sides are golden brown, scoop the donuts out with a frying spoon or spatula (something that is resistant to the heat, e.g. metal), and lay them on a wire rack lined with paper towels. The paper towels will soak up the excess fat.
Once the donuts look dry, but are still hot, roll them in a bowl of white sugar to coat them entirely, then let them continue to cool.
Fill the Donuts
Once the donuts are completely cool, use a long thin object (like a metal straw or a chopstick) to poke a hole in the side of the donuts and move it around to create extra space for your custard - we want these babies to be FULL of custard, so you need to give it somewhere to go.
Remove your pastry cream from the refrigerator and give it a mix to restore the texture. Put it in a piping bag with any kind of nozzle.
Push the nozzle into the hole you created earlier and squeeze gently. You will feel the donut start to feel heavy, which means it's full of delicious custard! Pull the nozzle slowly out of the donut, leaving a pretty little blob of custard on the outside to show the delicious custard filling.
Notes
Ingredients Notes:You can use active dry yeast or instant yeast for this recipe. If you use instant yeast there is no need to activate it first, just add it straight into the bowl with the wet ingredients. Custard Notes:Make sure you whisk constantly while your custard is on the heat - if you let it sit you will end up with lumps of egg or burnt pastry cream!When your pastry cream is ready, you will be able to coat the back of a spoon and run your finger through it to make a line - the line will not fill in, it should stay visible. This means your pastry cream is cooked enough. If left to develop overnight, the custard has a much richer flavor - if you have time I highly recommend this! Donut Notes:It can be helpful to cut the parchment paper under the proofed donuts into little squares to help you slip the donuts into the oil without getting finger dents in them. Slide the parchment paper and donut onto a frying spoon or spatula (something that can withstand the heat of the oil - e.g. metal) and then slowly lower it into the oil while holding onto the corner of the parchment paper - the donut will slip off into the oil without any marks or dents! It's an extra step and is not necessary - but it ensures better results!