In a large bowl whisk together oil and sugar for about 3 minutes. Add molasses, soy milk and grated ginger and mix well.

Sift in all of the other dry ingredients, mixing about half way through. When all of the dry ingredients are added, mix until a stiff dough is formed.

Flatten the dough into a disk, wrap in plastic wrap and chill for an hour or up to 3 days in advance. If you chill longer than an hour you may want to let it sit for 10 minutes to warm up a bit before proceeding.

Preheat oven to 350 F. Lightly grease your cookie sheets or line with parchment paper.

On a lightly floured surface or on a sheet of parchment paper roll the dough out to a little less than 1/4 inch thick. Cut out your shapes with your cookie cutters and use a thin spatula to gently place on cookie sheets. Bake for 8 minutes.

Remove from oven and let them cool for 2 minutes on the baking sheet then move to a cooling rack. Wait until they are completely cool before icing. For the icing mix the icing sugar with the soy milk until you have a thick paste.