Preheat oven to 375˚. Line a 12-cup cupcake tin with liners, or lightly grease it with cooking spray.
In a large bowl, stir together the flour, 2/3 cup of the cocoa powder, the baking soda, 1 teaspoon of the salt, and sugar. Mix in the water, oil, 2 teaspoons of the vanilla extract, 1 tablespoon of the orange juice, the grated ginger, and the orange peel. Add the vinegar, and fold it in quickly to combine. The mixture will turn slightly foamy and paler in color. When the mixture turns slightly darker again, pour the batter into the prepared muffin tins. Bake 15 minutes, until a toothpick inserted into one of the cupcakes comes out clean. Allow to cool in the pan for 5 minutes, then transfer the cupcakes to a wire rack to cool completely.
Make the frosting while the cupcakes are cooling. Blend the margarine in a large bowl until creamy. Add the powdered sugar and last 1/8 teaspoon of salt, and mix well until incorporated. Stir in the last tablespoon of vanilla extract, the last tablespoon of orange juice, and the soy milk. Add the remaining 1/2 cup plus 2 tablespoons of cocoa powder, and blend until the frosting is smooth and creamy.
Frost the cupcakes when they're completely cool, and enjoy! Refrigerate any unused frosting in a covered container for up to a week.