To make the dough, in a small bowl, whisk together the flaxseed meal and 5 tablespoons of warm water. Set aside to rest and thicken for at least 5 minutes.
In a medium pot over medium heat, heat the soy milk until tiny bubbles form. Remove from the heat, stir in the vegan butter, and let cool to room temperature.
In a large bowl, mix together the yeast, 1 teaspoon of the granulated sugar, and 1⁄4 cup of warm water. Let the mixture sit for 10 minutes to activate the yeast.
Add the flaxseed meal mixture, soy milk mixture, and vanilla extract. Using a fork, stir in 21⁄4 cups of the flour, the remaining granulated sugar (1⁄4 cup minus 1 teaspoon), and the salt.
Gradually add the remaining 1 cup of flour and knead for about 5 minutes, until the flour is incorporated and the dough is smooth. Form the dough into a ball in the bowl, cover with a damp paper towel, and let rise for 1 hour in a warm place (ideally 80 to 90 degrees F).
To make the filling, in a small bowl, combine the vegan butter, brown sugar, and cinnamon and mash with a fork until the butter is fully incorporated and no chunks remain. Set aside.
On a floured surface, using a floured rolling pin, roll out the dough into a 12 × 15-inch rectangle. Using your fingers, spread the brown sugar mixture evenly across the dough. Starting at one of the shorter sides, tightly roll the dough so you have a 12-inch-long roll. Pinch to seal. With a sharp knife, cut the roll into 12 equally sized slices and place them on a baking sheet lined with parchment paper or a silicone mat. Cover with a damp towel or paper towel and let rise for 1 to 2 hours, until doubled in size.
Preheat the oven to 350 degrees F. Bake the rolls for 20 minutes or until they are golden brown and a toothpick inserted in the center comes out clean. Do not overbake. Using a spatula, lift the rolls off the pan immediately to prevent the filling from sticking, and transfer to a cooling rack. Allow the rolls to cool fully before frosting.
To prepare the frosting, using an electric hand mixer, beat together the vegan cream cheese and butter in a medium bowl. Add the powdered sugar, vanilla extract, and salt and beat until the frosting is smooth and thick. Spread the frosting evenly over each cinnamon bun.