Heat the milk so it's warm, but not hot. (about 100° F - about 45 seconds in the microwave does the trick) and add it to a mixing bowl with 1 packet of dry active quick-rise dry yeast. Give it a stir and let it sit for a few minutes.
Add the melted vegan butter, sugar, and salt, and stir again until no butter clumps remain.
Slowly add 2 1/4 cups of flour, stirring until you get a soft dough that you can hold without it sticking to you. (You may need to add another tablespoon or two of flour until the dough can be handled without being sticky.)
Knead the dough on a floured surface for about 3 minutes, until soft but no longer sticky. (At this point, you can put the dough in the refrigerator for up to 4 days and finish the rest of the steps when you are ready.)
Place the dough in an oiled bowl, then flip it over so the dough ball is coated with a thin layer of oil.
Put the dough in a warm spot to rise. (I usually turn on the oven to 150° F for a few minutes to get a little heat in there, then turn the oven off and put the dough in the oven to rise for about 1 1/2 hours.)
Once the dough has doubled (usually about 1 1/2 hours, depending on how warm it was during rising), punch it down and roll it out on a floured surface into a large rectangle about 9x14 inches.
In a small bowl, mix 1/3 cup brown sugar with 2 tsp cinnamon, and set aside.
Melt 3 tbsp of vegan butter, then spread it evenly over the dough and sprinkle with the cinnamon-sugar mixture.
Tightly roll the dough into a log, then cut it into about 1 1/4-inch pieces to form 9-10 even rolls.
Line a pie dish with parchment paper. Melt 1/3 cup of vegan butter, then mix in 1/3 cup of brown sugar and spread the mixture over the parchment-lined pan. (You can also give it a sprinkle of cinnamon and add 1/3 cup of crushed nuts to this, too, if you choose.)
Arrange the sticky buns in the pie dish so they are just barely touching each other, and bake at 375° for 25-30 minutes, until they are slightly golden brown on top.
Allow to cool in the dish for about 10 minutes, then lift the parchment paper and flip the sticky buns onto a tray so the sticky side is facing up.
Notes
The amount of flour needed may vary slightly. Go by the feeling of the dough more than the measurement. Add just enough flour that your dough is no longer sticky and you can knead it without it sticking to your hands, but remains very soft.
The warmer the air, the faster your dough will rise. About 80°- 90° F is a great temperature for this. Turn your oven on for about 3 minutes until it is just barely warm, then turn it off. Place the dough in the oven to rise.
You know that your dough is ready to roll out when it has doubled in size.
Don't put more butter and sugar than the recipe recommends on the dough, or it will just fall out and make a mess.