Mix warm soy milk, dry yeast, and cane sugar in a large bowl. Let it sit for 5 minutes, then add melted coconut oil, vanilla extract, egg replacer, flour, and salt. Mix to form a shaggy dough.
Turn the dough out onto flat surface, and knead for 10 minutes.
Place the dough in a lightly greased bowl and cover with a towel or cling wrap. Let it rise in a warm place for 60 to 90 minutes, until the dough double in size.
On a lightly floured surface, roll out the dough into a rectangle, about 25cm x 35cm (10in x 13in). Spread melted vegan butter, and sprinkle cinnamon and cane sugar evenly.
Starting from one of the short end, roll up the dough into a tight log. Cut the log into 6 evenly sized pieces. Use a serrated knife to make even clean cuts.
Place the rolls in a baking dish lined with parchment paper, cover, and let it rise in a warm place for 30 minutes.
In a preheated oven at 180C / 350 F, bake the rolls for 20 minutes, until lightly golden on top.
For the icing, mix powdered sugar, soy milk, and vanilla extract. Drizzle over the rolls while they are still warm. Serve while warm. Enjoy!