For better results, cut the butter into small pieces and place it in the freezer for 15 minutes. Using very cold, diced butter will make your biscuits light, flaky, and buttery.
Preheat the oven to 425ºF (220ºC) and line a baking sheet with some parchment paper. Set aside.
Mix the non-dairy milk and vinegar in a bowl and let it sit at room temperature for at least 5 minutes. After this time, the milk will thicken and curdle.
Add the flour, baking powder, sugar, and salt to a large mixing bowl or food processor. Whisk or pulse until combined.
Add the cubed vegan butter to the dry ingredients and either use a pastry cutter to cut it into the mixture or pulse several times in a food processor until coarse crumbs form. If using a food processor, transfer the mixture to a large bowl.
Pour the milk and vinegar mixture into the bowl. Gently stir until almost combined, but do not overmix. The dough will be quite moist and sticky, and not form a clean ball at this stage.
Transfer the dough to a floured work surface and gently bring it together with generously floured hands. The dough will become sticky as you bring it together. Have extra flour nearby and use it often to flour your hands and work surface, but do not add too much or the vegan biscuits will be dry.
Gently flatten the dough into a ¾-inch (about 2 cm) thick rectangle. Fold one side into the center, then the other side. Turn the dough horizontally and flatten it into a ¾-inch (about 2 cm) thick rectangle again. Repeat the process two more times.
Cut into 2.5-inch (6.35 cm) circles using a biscuit cutter, but do not twist the biscuit cutter when pressing down into the dough. Re-roll the scraps until all the dough is used. You should have about 8-10 biscuits.
Place the vegan biscuits onto the prepared baking sheet at least an inch (2.5 cm) apart. You have the option to gently brush the tops with milk, but it's not necessary.
Bake for 12-15 minutes or until the tops turn a beautiful golden brown. Be careful not to burn them! Remove from the oven and serve warm.