Preheat oven to 350°F. Line a muffin pan with paper liners.
In a medium bowl whisk together 1 cup milk (or coconut milk), 3/4 cup sugar, 1/3 cup canola oil, and 1 teaspoon vanilla extract until the sugar is mostly dissolved and the mixture is slightly foamy.
In a separate bowl sift together 1 cup all-purpose flour, 1/3 cup dark cocoa powder, 3/4 teaspoon baking soda, 1/2 teaspoon baking powder, and 1/4 teaspoon salt.
Add the dry ingredients to the wet ingredients in two additions, mixing after each addition until just combined and no large dry streaks remain (do not overmix).
Spoon the batter into the prepared liners, filling each about 1/4 cup.
Bake for 18–20 minutes, or until a toothpick inserted into the center comes out clean. Remove from oven, transfer cupcakes to a cooling rack, and let cool completely before frosting.
While cupcakes cool, melt the 2 ounces dark chocolate (microwave in short bursts or use a double boiler) and let it cool slightly so it is warm but not hot.
Make the frosting base: in a mixing bowl, cream 1 cup butter (room temperature) until smooth and fluffy, about 2–3 minutes. Add 1/2 tablespoon of the 2 tablespoons soymilk and mix to combine. Divide the butter mixture evenly into two bowls (one half for mint frosting, one half for chocolate frosting).
Mint frosting: to one half of the butter, add 4 drops creme de menthe flavoring, a few drops green food coloring to reach the desired color, and 1/2 cup of the 1 1/4 cups confectioners’ sugar (add in two 1/4-cup additions), beating until light and fluffy, about 3–5 minutes. Transfer this mint frosting to one side of a piping bag.
Chocolate frosting: to the other half of the butter, add the cooled melted chocolate and beat until fully incorporated and fluffy, about 3–5 minutes. Add the remaining 3/4 cup confectioners’ sugar a little at a time, mixing after each addition. Add 3 drops creme de menthe flavoring and the remaining 1 1/2 tablespoons soymilk as needed (add gradually) and beat until smooth and fluffy.
Spoon the chocolate frosting into the other side of the same piping bag so both frostings are present (or use a second piping bag if preferred).
Pipe the two-color frosting onto the cooled cupcakes, top each cupcake with a halved Andes mint (cut on the diagonal), and serve.