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 int 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.
When you’re ready to cook the donuts, 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 or so.
Meanwhile make your toppings.
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, sugar and vanilla into a small saucepan and melt together. When it has melted add the hot water a tablespoon at a time until the glaze reaches a runny consistency.
Preheat oven to 350ºF
Place donuts and holes onto greased baking sheet. Bake for 12-13 minutes or until golden brown. Flip once during cook time.
While the donuts are still hot add the various toppings: Dip donuts into 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. Transfer to cooling rack for 5 minutes to allow glaze to set.