Combine warm water and yeast in measuring cup. Let sit in warm area for 5 mintes to proof yeast.
Combine flour, sugar, yeast/water mixture, eggs and salt in large mixing bowl.
If using a stand mixer use the dough hook attachment to mix on a medium speed for 8-10 minutes or until the dough is pulling away from the sides of the bowl. You can also do this by hand using a wooden spoon, dough whisk or similar. *If dough is too wet and is dripping, not binding, add more flour a little at a time while mixing until the dough comes together.
Leaving the mixer on a medium speed, add the softened butter a little at a time making sure to fully incorporate the butter into the dough each time. When all the butter has been added, leave the mixer running on a low-medium speed for a further 5 minutes or until the dough is very smooth and elastic. If you’re not using a mixer, knead the dough by hand for 8-10 minutes.
Cover the mixing bowl with plastic wrap and leave the dough to rise and double in size. This will take approximately 1 hour depending how warm your kitchen is. It may take up to 3 hours if your kitchen is very cold.
When the dough has risen, punch the air out of it and put it in the fridge for 24 hours. *See notes.
Line three baking trays with floured parchment paper.
Roll the dough out until it is about 1/2 inch thick then use a 3.5 inch donut cutter (or something round, like a glass) to cut 10-15 donuts out of the dough. Use a donut hole cutter or an upturned piping nozzle to cut the donut holes from the middle of each donut. Anything small and round will work just as well.
Transfer 5 donut rings and 5 donut holes to each baking tray, leaving space in-between them. Loosely cover with plastic wrap and leave to rise for an hour.
Prepare topping/glaze before air frying donuts.
To make the chocolate glaze, put the powdered sugar, cocoa powder and milk into a small bowl and whisk together until smooth.
To make the Cinnamon coating, mix the sugar and cinnamon in a small bowl. In a separate bowl, melt the butter – you will use this to brush the donuts with later to give the cinnamon sugar something to stick to.
To make the vanilla glaze, put the butter and sugar into a small saucepan and melt together. When it has melted add vanilla then hot water a tablespoon at a time until the glaze reaches a runny consistency. (You can also just microwave the butter to melt then whisk in powdered sugar, vanilla and water)
Lightly grease the tray of the air fryer with oil.
When the donuts have puffed up, carefully transfer them into the air fryer basket, you should be able to fit 3 or 4 depending how big your air fryer is.
Air fry at 350ºF for 2-3 minutes then flip them over and air fry at 350ºF for 2 more minutes. At this point they should be done or may need 1-2 more minutes depending on your air fryer. The donuts should be golden brown in color. Repeat with the remaining donuts and holes.
While the donuts are still hot add the various toppings: Dip some of the donuts in the chocolate and vanilla glaze. Brush the others with the butter that you melted earlier and dip them into the cinnamon sugar. Do the same with the donut holes.
FOR OVEN BAKED DONUTS
Follow preparation instructions for dough.
Preheat oven to 350ºF
Place donuts onto greased baking sheet. Bake for 12-13 minutes or until golden brown. Flip once during cook time.