Preheat oven to 350°F. Line a baking sheet with parchment paper.
In a large bowl, whisk together the flour, sugar, cream of tartar, baking soda, and salt.
Cut the vegan butter into small cubes and add to the flour mixture. Use a pastry cutter or two forks to work the butter into the flour mixture until you get a grainy/mealy texture.
Gently stir in the vanilla extract and nondairy milk, try not to overmix. Fold in the dried cherries and chopped chocolate. The mixture should be firm and sticky.
Place the dough onto the prepared baking sheet and form it into a 8" diameter circle. Cut the dough into eight triangle slices with a knife, still keeping it's form together.
Bake for 15-20 minutes. Remove from the oven, re-cut the slices, and pull them apart slightly. Place them back into the oven and bake for an additional 7-10 minutes, until tops are lightly browned. Let cool for 5-10 minutes before serving.