Mix the nondairy milk with the vinegar and set aside in the refrigerator for a couple of minutes to curdle.
Place the flour in a bowl with the baking powder, baking soda and salt. Whisk together. Add the butter to the bowl and, using a fork or a pastry-cutter, "cut" the butter into the flour until you have a coarse mixture with a few pea-size pieces of butter. (Cutting the butter into the flour is just a fancy way of saying you press down on the pieces of butter with the tines or your fork or your pastry cutter to cut the butter into smaller bits)
Slowly, using a fork to mix, drizzle in the nondairy milk and vinegar mixture. You may not need all of the milk depending on your climate. Your dough should be moist enough to come together in a ball, but not wet.
Wrap the biscuit dough in cling wrap, flatten into a disc, and place in the refrigerator for at least 5-10 minutes.
Preheat the oven to 450 degrees F
On a floured surface, roll out the disc of the biscuit dough. The thicker you roll your dough, the taller your biscuits will be, so you have a choice here. The thicker you roll your dough, the fewer biscuits you'll get. I roll my dough about 1/2-inch thick and I get 12-14 two-inch biscuits, which is perfect for me. (If you are making gluten-free biscuits, don't roll out the dough. Instead, flour the surface well with gf flour, then pat the dough into a circle using your hands.)
Use a two-inch round cookie cutter to cut the biscuits and place them at least an inch apart on an unoiled baking sheet. Reroll any leftover scraps of dough and make more biscuits.
If desired, and this is optional, brush the tops of the biscuits with a mixture of 1 tbsp soy milk and 1 tbsp vegetable oil for a nice, golden-brown color.
Bake the biscuits for 12-14 minutes or until the tops are a nice, light gold. (If making these gluten-free, you will need to bake these around 18 minutes)
Serve hot, warm or at room temperature.