Preheat the oven to 350°F (175°C). Line the bottom and two sides of a standard loaf pan with parchment paper, and lightly grease it with canola oil, or any other neutral-tasting oil of your choice.
In a large mixing bowl, whisk together the flour, brown sugar, baking powder, baking soda, fresh ginger, ground ginger, cinnamon, nutmeg, cardamom, and salt until evenly combined and lump-free.
Make a well in the center of the dry ingredients, and pour in the plant-based milk, apple cider vinegar, plant-based yogurt, molasses, canola oil, and vanilla.
Using a rubber spatula, stir until just combined. Avoid overmixing to prevent a dense loaf.
Pour the batter into the prepared loaf pan and smooth the top with a rubber spatula or an offset spatula. Bake for 50-55 minutes, or until a toothpick inserted into the center comes out clean. Let the loaf cool in the pan for 12 minutes before transferring it to a wire rack to cool completely.
For the orange cream cheese frosting, stir the orange zest and optional Grand Marnier into the vegan cream cheese frosting until evenly distributed.
Once the loaf has fully cooled, spread the frosting over the top. Optionally garnish with additional orange zest. Slice and serve.