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.
While the dough is proofing, make the sautéed apples. Heat vegan butter in a pan, and cook the apples on medium-low for 3 minutes. Add maple syrup, cinnamon, nutmeg, and chopped pecans and cook for 2 more minutes, until slightly caramelized.
On a lightly floured surface, roll out the dough into a rectangle, about 25cm x 35cm (10in x 13in). Spread melted vegan butter evenly, and sprinkle cinnamon and cane sugar. Spread the sautéed apples on top.
Starting from one of the short ends, 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 25~30 minutes, until deep golden on top.Cool for 10 minutes before removing from the dish. For the icing, mix powdered sugar, maple syrup and soy milk. Drizzle over the rolls while they are still warm. Serve while warm. Enjoy!