In a stand mixer bowl, with a paddle attachment, (or a large bowl) add the warm water, sugar, and yeast. Mix together. Let sit for 5 minutes. Add in pumpkin and vanilla. Combine again.
Turn stand mixer to low and add 2 cups of flour, black cocoa powder, salt, and nutmeg. When almost all combined add 1 more cup of flour and combine again.
Switch to a dough hook and add 1 more cup of flour and mix just until combined. Add in butter 1 tablespoon at a time, mixing completely after each.
Let knead for 8-10 minutes on medium speed or until it doesn't stick to the bowl. It will pull away from the bowl. Still slightly sticky but not sticking to your hands.
Spray bowl, form into a ball and place ball inside. Cover with a towel or plastic wrap and let sit for 30 minutes in a warm, draft free place.
For the Custard Filling
While dough is rising, make custard filling. In a medium saucepan, add non-dairy milk, brown sugar, cocoa powder, and cornstarch. Whisk together.
Place pan over medium heat and let cook for 3-5 minutes until it starts to thicken, stirring occasionally. Add in vegan chocolate chips and butter. Stir constantly until melted completely. Remove from heat and stir vanilla into mixture.
After 5 minutes, stir the mixture. Wait an additional 5 minutes and stir again. Place plastic wrap on top of the mixture (touching it). Place in fridge until completely cooled.
To Make Doughnuts
After 30 minutes, lightly flour a surface and roll out dough to be about a half an inch thick. Then using a 3.5" donut cutter, cut out your donut shapes. Fold dough back up and then roll out again to cut out more donuts until no dough remains.
Place each cut out on a baking sheet and then cover and let rise again for 15-20 minutes.
Heat oil up to 350-375 degrees F. Fry for about 1 minute on each side (*Use a timer since this is black dough to make sure it's cooked properly). Carefully remove donuts from hot oil and place on a cooling rack with a sheet pan under it to catch the oil or a towel lined plate.
Once cool to touch, add 1/2 cup sugar to a bowl and toss donut in sugar to coat.
Repeat until all donuts are cooked and coated.
Once donuts and filling are completely cooled, then, use a piping bag and a narrow piping tip fill the inside of the doughnut, pulling back as it fills until it's out. Repeat with all doughnuts.
Serve immediately or let cool to room temperature and store in an air tight container for up to 2 days.