In a large mixing bowl, combine warm soy milk, molasses, and active dry yeast. Let sit for 10 minutes until frothy.
Whisk in the melted vegan butter, ground ginger, cinnamon, and salt.
Gradually add flour one cup at a time, mixing until a dough forms. Knead by hand or with a dough hook for 7 minutes until smooth and elastic.
Place dough in a lightly greased bowl, cover with a damp cloth, and let rise in a warm spot for 90 minutes or until doubled in size.
Punch down the risen dough and roll out on a floured surface into a 12x18 inch rectangle.
Spread the softened vegan butter evenly over the dough. Combine brown sugar and spices in a small bowl, then sprinkle evenly over the butter.
Roll the dough tightly starting from the long edge. Cut into 12 even slices using unflavored dental floss or a sharp serrated knife.
Arrange rolls in a greased 9x13 inch baking pan. Cover and let rise for an additional 30 minutes.
Preheat oven to 350°F (175°C). Bake rolls for 22-25 minutes until lightly golden.
Whisk together powdered sugar, plant milk, and vanilla until smooth. Drizzle over the rolls while still warm.