Microwave the soy milk for about 1 minute if refrigerated, so that it's as warm as bath water. You don't want it to boil, so watch closely. If you don't have a microwave, warm it in a small pan.
In a large bowl, or the bowl of a stand mixer, stir together the warm soy milk, yeast and sugar. Let the mixture sit for 3-4 minutes, until it's a bit frothy.
To the bowl with the yeast mixture, add the applesauce, softened vegan butter, vanilla, salt and 2 cups of flour. Mix on low speed with a dough hook, or by hand with a large wooden spoon, for a few minutes, then add the rest of the flour and continue to mix.
If using a stand mixer, beat with the dough hook for about 2-3 minutes. If you are making them by hand, mix it as well as you can with a spoon, then transfer to a lightly floured surface and knead the dough for about 5 minutes until you have a nice soft ball of dough.
Lightly grease a large bowl (I use non-stick spray) then place the dough in the bowl. Cover with a clean kitchen towel, then allow to rise in a warm place for 30 minutes. I preheat my oven to 170℉, then turn it off and place the bowl inside with the door cracked.
After 30 minutes, punch the dough down. Place it on a lightly floured surface and roll it about 1/2 inch thick. Use a donut cutter or a large biscuit cutter to cut the donuts. You should get about 16-18.
Line a large baking sheet or two with parchment paper, and place the cut donuts on the pans. Cover with a large towel for about 15 minutes while you heat the oil.
Heat 2-3 inches of oil in a large pan or pot until it reaches 375℉. I highly suggest using a thermometer so you get this just right.
Add a few donuts at a time to the oil and cook for about 1-2 minutes on each side, until golden brown, being careful not to let them get too dark and burnt. If the oil is hot, this won't take long. Be careful of hot oil!
Place the cooked donuts on a cooling rack with a pan or parchment paper underneath to catch any oil drippings. Repeat until all donuts are fried.
Cut a deep slit into the side of each donut, then use a piping bag with tip to pipe jelly into each one. Dust the tops with powdered sugar or roll in granulated sugar. Serve and enjoy!