Prepare flax egg. Add ground flaxseed to a small bowl with 3 tablespoons of warm water. Mix and let sit for at least 5 minutes.
Proof the yeast. Add the yeast to a medium bowl. Warm the milk. It's important here to make sure the milk isn't hot or cold. It must be warm. Add the warm milk, stir gently, and set aside for 10 minutes.
Whisk together the dry ingredients in a large bowl. Mixing the flour, sugar, baking powder, salt, and cinnamon.
Mix together the filling ingredients- brown sugar, melted vegan butter, and cinnamon.
Prep the dough. Once it's been 10 minutes and the yeast has proofed, add the flax egg, melted butter, and apple cider vinegar to the bowl with the yeast. Stir, then pour this mixture into the bowl with the flour. Stir to combine. Eventually it will become too thick for your whisk or spoon- switch to your hands, forming a ball. If the dough is too dry add more milk. If it is too wet, add a little extra dough at a time.
Lay out a large sheet of parchment paper and brush oil over top, lightly. Roll out the dough ball into a rectangular shape. Using a rolling pin is helpful here. If you don't have one, use your bottle of apple cider vinegar- just make sure it is shut tightly! Brush melted butter over top, lightly.
Spread the filling mixture over the dough leaving space around the edges, about ½-1 inch. Then begin to roll one end and lift the parchment paper to guide you as you roll the rest of the dough.
Once you have a long roll, make sure the seam is face down. Cut off the ends of the roll if they are not straight and don't contain any filling. You want even ends. Then slice the dough into 9 rolls.
Grease an 8-inch round cake pan. Place the rolls into the pan and cover it with a kitchen towel. Place it on the oven while you preheat it to 350F. Set a timer for 1 hour.
After an hour has passed, the rolls should have grown in size. Place them in the oven to bake for 25 minutes.
While the cinnamon rolls are baking, make the frosting. In a medium bowl, stir the powdered sugar, vegan butter, milk, vanilla extract, and salt until well combined and smooth.
When the cinnamon rolls are done, remove from the oven and place on a cooling rack for a few minutes. Once cooled a bit, frost the cinnamon rolls and enjoy!