Hydrate the yeast. Mix yeast packet with the warm water and sugar, and let the foam double in size.
Make the brioche dough. Mix the flour, sugar, water, activated yeast, lemon zest, salt and eggs into the bowl of an electric mixer with a dough hook attachment and mix on medium speed for 1-2 minutes, until it's all combined. Then turn up the speed to medium high and let it run for about 5 minutes, or until the dough starts coming away from the sides and forms a ball. Turn off the mixer and let the dough rest for a minute. Slowly add the butter to the dough, about 25g at a time. Once it is all incorporated, mix on high speed for 5min until the dough is glossy, smooth and very elastic when pulled.
Proof the dough. Cover the bowl with saran wrap and leave to proof in the bowl until it has doubled in size - about 1-2 hours. Punch down the dough – then re-cover the bowl and put into the fridge to chill overnight. The next day, take the dough out of the fridge and cut it into equal, quarter or silver dollar size pieces (you should get about 50). Roll them into smooth, taut, tight buns and place them on a floured baking tray, leaving plenty of room for them – so they don't stick together while they proof. Cover lightly with Saran wrap and leave out in a 75F room for about 4hr, or until about doubled in size.
Fry the donut holes! In a big cast iron pot, prepare the deep fryer; fill it up to the halfway point with the oil. Heat the oil to 350F, then carefully remove the doughnuts from the tray by sliding a floured pastry scraper or fish spatula underneath them, taking care not to deflate them, and put them into the oil. Don’t overcrowd the fryer – do two to three per batch, depending on the size of your pan.
Toss with sugar. toss the donuts with a mixture of powdered sugar and cinnamon!