Preheat the oven to 180 degrees C/350 F.
Add the flour, coconut sugar, carrot, pecan nuts, baking soda, baking powder, cinnamon, ground ginger and nutmeg to a large mixing bowl and mix. In a separate mixing bowl, whisk together the plant milk and melted vegan butter.
Add the wet ingredients to the dry and mix them together until thoroughly combined.
Pour the batter into two 8-inch cake tins. Bake in the preheated oven for 35-40 minutes, until a toothpick comes out clean.
Meanwhile, prepare the frosting. Add the vegan butter to a mixing bowl and whisk with an electric mixer until light and fluffy, gradually adding in the icing sugar. At the end, add the orange juice and vanilla essence, whisking once more to incorporate.
Assemble the cake. First, ensure the cake has cooled down fully before adding the frosting by leaving the sponges on a cooling rack or in the fridge for around 15 minutes. Then, spread around half of the icing on one of the sponges. Layer with the second sponge, and spread the rest of the icing on top.
Serve immediately or store in the fridge in an air-tight container for up to 4 days.