First make the donut dough: Sprinkle the dry yeast over the warm milk with a pinch of sugar & allow to prove for about 5 minutes until slightly frothy
Melt the vegan butter then get the flax meal combined with the hot water & let it stand to thicken for 5 minutes
In a mixer fitted with a dough hook attachment combine all the donut ingredients including the yeast/milk mixture & the semi soft vegan butter
Mix on low speed until everything is incorporated for about 30 seconds, then scrape the bottom & sides of the bowl to help it along & mix on low to medium for 8 more minutes
Place the dough into a lightly oiled bowl & set in a warm spot, covered for 30 minutes
After 30 minutes, fold the dough over onto itself 4 times from the corners stretching gently to form gluten & then continue the rest for another 30 minutes.
Meanwhile prepare the buttercream according to the recipe on that post & add the 1 cup crushed cookies at the last stage of mixing~ reserve at room temperature (the other 1/4 cup is for dipping the finished donuts at the end)
Once the dough has almost doubled in size & is nice & fluffy & puffy turn it out onto a lightly floured surface & roll it to ¼" - ½" thick
Cut the donut dough out with a 3 or 4" biscuit cutter & place each one on a parchment lined sheet pan and allow them to rest & rise some more for 30 minutes~ Only then will you begin heating the frying oilIt is not great to re-roll this dough so I like to take the scraps and twist them up to make crullers. In a large, deep heavy bottom sauce pot heat 3 cups of frying oil to approximately 375°F (190°c)
Fry the donuts for approximately 1 minute on each side using a metal or wooden utensil to do the flipping. Be very careful working with hot oil~it is very dangerous if it spills or splatters on your skin.
Remove the donuts with a slotted metal spider utensil or spatula to a cooling rack or a sheet pan lined with paper towels to absorb the excess oil.
Fill the cooled donuts with the cookie buttercream then ice in confectioner's sugar glaze & dip in crushed cookies