These are not vegan but you definitely could convert them: sub out chilled refined coconut oil for the butter, and almond milk + apple cider vinegar for the milk.
2 cups Flour
4 tsp baking powder
1/4 tsp baking soda
3/4 tsp salt
4 tbsp butter
1 cup milk + 1 tbsp apple cider vinegar
First, combine the milk & the vinegar and set aside until good and curdley. 15-20 minutes is generally enough time for this, but if you don't have that much time, it's ok, too. You want to simulate buttermilk here, if you can.
Mix the flour & dry ingredients together. Use your hands to cut in the butter till it looks like small bread crumbs. Make a well, and add the milk mixture, and stir just till everything comes together. It'll be very sticky! Distressingly so, but do not worry!
Turn the dough onto a well floured surface, flatten it out into a rectangle that's about an inch thick or so. Turn it over on itself, like you're folding a letter. Flatten it again and fold it over again; repeat one more time for a total of three letter turns. Flatten it back down into a 1" thick rectangle.
If you have time, chill the dough now - this will help make it extra flaky, but if you don't have time, it'll still be fine. When you're ready, cut the dough into 2"x2" squares. Place them on a baking sheet about an inch apart from one another.
Bake until they're tall and pale gold on top - if you have a good gas range, about 15-20 minutes. If you have a temperamental electric oven, maybe more like 12 minutes - those things can run hot. There you go! Fancy delicious biscuits! Probably about 6-8 of them, depending on the size.