Start with mixing sugar with lukewarm milk then sprinkle yeast on top. Make sure the kitchen is nice and warm, and in 10 minutes the yeast should foam.
Place the yeast mixture into your stand mixer with the kneading hook on, then mix it together with the egg and egg yolk.
Mix in dry ingredients; flour, and salt, and start kneading until the dough comes together.
Slowly start to add in room temperature (soft) butter chunks piece by piece. Knead the dough for another 10 minutes on medium high speed until the dough becomes elastic and shiny and no longer sticky.
Move the dough into a bowl, cover it with plastic wrap or a tea towel. Let it rise ideally in the fridge overnight or at room temperature for 1-2 hours.
After the dough has risen, knock the air out, and gently knead the dough for a few seconds.
Roll the dough on a lightly floured surface into ¼ inch (0.6mm) thick, and with the help of a cookie cutter, cut out approx. 3-inch / 8 cm donut circles, then cut out the middle with a smaller sharp object (I am using the back end of a piping nozzle). You can also use a donut cutter. Use a small amount of extra flour while shaping the dough, if needed.
Place the donuts onto square sheets of baking paper. Any leftover dough can be re-rolled and re-cutted, continue with the process until you have dough left.
Proof the dough for the second time now at room temperature. Proofing might take 1-2 hours depending on the temperature of your kitchen. Chose a warm spot but avoid direct heat and sunlight.
Once the donuts are nicely puffed up, heat vegetable oil in a heavy-bottomed pan over medium heat. The ideal oil temperature for baking donuts is 180C/356F or between 175-185C / 347-365F. Use a thermometer.
Depending on the size of your pan, place 3-4 donuts in the oil at a time, leaving enough space around them. Fry the donuts on each side for about 2 minutes or until nice and brown.
Place the fried donuts on a wire rack lined with paper towels to soak up any excess oil. While they are still hot, toss the donuts in granulated sugar. Serve them fresh.
Store the donuts in an air-tight container at room temperature for 1-2 days.
Notes
INGREDIENT NOTES
Use always unsalted butter in baking, in this recipe butter needs to be at room temperature so soft enough to be able to knead into the dough.
Fresh or dried yeast can be used. Please check my baking guide for more details on how to bake with yeast.
Use the milk, butter, and egg at room temperature in order for the ingredients to properly emulsify.
Since rum donut is effectively a sweet bread, use high protein content bread flour.
TECHNIQUE NOTES
For activating the yeast (whether it is dried or fresh), make sure that the milk is lukewarm and your kitchen is also nice and warm.
You will knead the dough for about 10 minutes in a stand mixer. The dough is ready when it is shiny, elastic, and does not stick to your fingers any longer. Do not add more flour to the dough. If it sticks too much, continue kneading.
The first proofing ideally should happen in the fridge overnight for the best flavor and texture. It will also mean that you work with cold dough when shaping the donuts, which is less sticky and easier to shape.
Second proofing is necessary for the perfect rise = fluffy texture
The oil temperature is critical; use a thermometer. Too hot? It will burn the donuts and they might stay raw in the middle. Too cold? The donuts will soak in too much oil and, again, might stay raw in the middle.