First, make the cake. Preheat oven to 350F and spray three 6" round cake pans with nonstick baking spray.
In a small bowl, whisk together the ground flaxseed with the water and set aside to thicken.
In the bowl of a stand mixer, combine the flour, baking powder, baking soda, salt, and sugar.
Add in the vegan butter, and beat on low until it's incorporated and has a sandy texture.
In a small bowl, whisk together the oil, flaxseed mixture, nondairy yogurt, vanilla extract, and peppermint extract, and add them to the dry ingredients. Mix until combined.
Pour in the nondairy milk, and beat on medium-low until smooth and creamy. Finally, gently fold in the chocolate chips.
Divide batter evenly among the 3 pans, and bake for 30-35 minutes until cake is set in the center and a toothpick comes out clean.
When the cakes are completely cooled, you can make the frosting. In the bowl of a stand mixer, beat the shortening, vegan butter, and vanilla extract together until completely smooth and creamy. Add in the powdered sugar, 1 cup at a time, until a thick frosting forms. Add in the salt. It is normal to need to add 1-2 tablespoon of milk to get the right consistency.
If you want to make the striped effect, transfer about ⅓ of the frosting to a separate bowl so that it can stay white. Color the rest of the frosting mint green - I used 1 drop of teal food coloring to 2 drops of leaf green coloring.
To assemble the cake, trim off the top of the cakes if needed to make sure they are level and flat.
Place one cake on your cake stand or platter, and spread some white frosting on top. Repeat with all.
Next, cover the cake with a layer of frosting for the crumb coat. Cover the cake, being sure to fill in any gaps between the layers. Use a bench scraper to remove any excess (remember we want this layer to be pretty thin).
Let the cake chill for 15-20 minutes so the crumb coat can solidify, then you can frost the "final" frosting! Cover the cake with mint green frosting, and use a stripe comb to remove the excess. This layer does not have to be perfect. Chill once again until solid.
Finally, place your reserved white frosting in a piping bag and pipe it into the indentations to create the stripes.
Use the bench scraper and gently remove the excess frosting until the sides and top of the cake are nice and smooth.
Place the cake back in the fridge for 10-15 minutes before adding on the ganache.
To make the ganache, place about ½ cup of dark chocolate chips in a microwave-safe bowl. Add in a splash of nondairy milk, and microwave in 20 second intervals until smooth and creamy. Add more milk and keep stirring if the mixture is too thick.
Decorate your chilled cake with the ganache - I just use a spoon for an easy drip. Place the cake back in the fridge for a few secondsbefore decorating the top with frosting as you want the ganache to solidify.
Use any extra frosting to decorate the top (or make another half batch). I used a 1M tip and piped in a circular motion to get the crown of frosting around the edge. Finish the cake with mini chocolate chips on top!