Preheat your oven to 350F. Grease two 8-inch cake pans and set them aside.

In a large bowl, mix together the flour, cocoa powder, sugar, baking soda, and salt. Add the vinegar, vanilla extract, oil, and water to the dry ingredients. Mix until smooth and well combined.

Pour the batter evenly into the prepared cake pans. Bake for 25-27 minutes, or until a skewer inserted in the center comes out mostly clean. Allow the cakes to cool completely.

While the cakes cool, prepare the frosting. In a large bowl, beat the softened vegan butter until smooth. Gradually add in the powdered sugar, continuing to beat until combined. Mix in the peppermint extract and green food coloring. If the frosting is too thick, add a little milk until you reach the desired consistency.

To assemble the cake, cut each cooled cake in half horizontally to create four layers. Place the first cake layer on a serving plate and spread a thin layer of frosting on top. Repeat with the remaining cake layers and frosting, finishing with frosting on the top layer.

Refrigerate the cake for about 30 minutes to allow the frosting to set.