Mix the non dairy 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. You can also do this in the food processor--pulse the flour and butter three to four times, for five seconds each time, no more, until the butter has broken down into smaller bits.
Slowly drizzle in the nondairy milk and vinegar mixture, and mix with a fork until the dough forms. If doing this in the food processor pour the milk through the feed tube while turning on the "pulse" button in short bursts. You may not need all of the milk. The dough should be moist enough to come together in a ball, but it should not be too wet.
Wrap the biscuit dough in cling wrap, flatten into a disc, and place in the refrigerator for at least 5-10 minutes. Meanwhile, set the oven to preheat to 450 degrees Fahrenheit/230 degrees Celsius.
On a floured surface, roll out the dough about ½-inch thick. Use a cookie cutter to cut out biscuits. Roll up dough scraps and cut more biscuits. You should get about 10-12 biscuits.
Place the biscuits at least an inch apart on a baking sheet. You can brush a mixture of one teaspoon oil with one teaspoon non-dairy milk on the biscuits to help them color. Bake for 14 minutes until fluffy and golden.
Serve hot or warm.