Preheat the oven to 350 degrees F and line a baking sheet with parchment paper.
Melt the vegan butter, then add it to a large bowl with the sugar and whisk well. Now whisk in the vanilla, peppermint extract, cornstarch and soy milk until well combined.
Over the bowl with the wet ingredients, sift in the flour, cocoa powder, baking soda and salt. Stir to combine. The dough will be quite thick, use your hands if needed. Now fold in the chocolate chips and candy cane pieces, leaving some to place on top of the cookies for decoration if you want. Again, you may need to use your hands to really get the chocolate chips/candy cane pieces incorporated.
Scoop about 2 tablespoons of the dough at a time, roll into a ball, then flatten a bit on the baking sheet. They will spread out more as they bake. Decorate with a few more chocolate chips and/or candy cane pieces on top, if desired.
Bake for 10-12 minutes, until they look cooked on top. They will seem too soft, but will firm up as they cool. Let them cool on the baking sheet for 5 minutes, then transfer to a cooling rack to cool completely. Enjoy!
Store leftover cookies in a covered container for 3-4 days. They also freeze well.