Combine room-temperature dairy-free milk and a tablespoon of sugar in a bowl and microwave them for about 1 min. Use a thermometer to measure the temperature and ensure that they are between 105-110*F.
Once you have reached the desired temperature, add the yeast to the mixture. Cover the bowl with a towel and let it sit for 5-10 minutes so the yeast can activate.
To a large bowl, add the flour, sugar, butter, salt, and the activated yeast mixture. Start kneading the dough until everything is well combined.
Once you've created your dough, cover the bowl of dough with a towel and leave it in a warm place for 45 minutes, until the dough has doubled in size.
While the dough is rising, begin making the apple filling. Finely chop the apples, then add them to a large pan over medium heat and add the chopped pecans, sugar, spices, and vanilla. Cook for about 10 minutes, until the apples soften and release their juices. Then add the cornstarch and whisk it through the apple mixture until it thickens. Make sure to break up any clumps
Note: don't add the butter to the pan of apples. You will be spreading that on top of the dough instead.
Transfer the apple mixture to a bowl and place in the freezer for 10-15 minutes to allow it to cool off. You don't want to add the apples to the dough when they are too hot.
After the dough has doubled in size, take it out of the bowl. Sprinkle a clean surface with flour and place the dough on top. Knead the dough using your hands until it becomes less sticky. Add extra flour, a little at a time, if needed.
Use a rolling pin to roll out the dough into a rectangular (about 15 x 10 inches long).
Spread the room temperature vegan butter on top of the dough, then spread the apple mixture evenly on top, leaving about ½ an inch border around the perimeter.
Gently roll the dough starting from the longer side. Slice the dough into 12 equal-sized pieces. I find that using dental floss works best for slicing (make sure to use unscented floss).
Transfer the rolls to a pan. Cover them with a towel and place them somewhere warm for 45 minutes.
Preheat the oven to 350*F.
Once the rolls have grown in size, place them in the oven and bake for 30-35 minutes, until the edges are golden.
While the rolls are baking, whisk together the frosting ingredients.
Once the rolls have cooled off, add a large dollop of frosting on each roll and dig in!