Preheat oven to 425 degrees F. Line a baking sheet with parchment paper.
In a small bowl, add together the milk and vinegar. This makes vegan buttermilk. Let sit together for 5-10 minutes.
In a separate large bowl, add flour, vegan cheese, baking powder, baking soda, and salt. Whisk together. Grate in your frozen butter to the bowl. After about every 4 tbsp, fold the butter in with flour (this helps it not clump and stay cold). Stir together one last time to make sure well combined.
At this time, your buttermilk from Step 2 should be ready. Add in ⅓ cup maple syrup into buttermilk mixture. Add to the flour mixture and stir with a spatula until a shaggy dough forms. Careful not to overmix.
Onto a lightly floured surface, dump out the bowl. Use yours hands to gather the dough together and press into a rectangle. The dough should be scraggly/crumbly. Press the dough down to about 1 ¼ inches thick.
Fold the top ⅓ of the dough into the middle. Then, fold the bottom ⅓ to the middle. (Similar to how you would fold a paper. Flour dough a little if sticky. Press the dough out to 1 inch thick and repeating folding process. Trim off the rough edges to square off the sides to help with the rising. Then cut into 8 equal portions. Transfer to prepared baking sheet, spacing biscuits evenly. Place into the freezer for 15 minutes.
Remove from freezer. Bake for 18-22 minutes or until golden brown.
While cooking, in a small bowl, combine 2 tablespoon of each melted vegan butter and maple syrup together. Then brush the tops lightly with the mixture.
Serve immediately or let cool and store in an airtight container.