Combine the flour, baking powder, and salt in a mixing bowl. Stir well and set aside.
In a cup, combine the yogurt and water and whip with a fork until completely mixed and smooth. Stir in the vinegar. Place in the refrigerator to chill while completing the next step.
Peel the sweet potato and cut into 1/2 inch thick slices, then cut the slices into wedges. Boil in a saucepan full of water for about 20-25 minutes until completely soft. Drain, and use a fork to mash and whip the potatoes until they are completely pureed. Let chill in the refrigerator for 10-15 minutes.
Cut the shortening into the dry mixture with a fork until well mixed (there should be tiny clumps throughout). Measure out 2/3 cup of the potato pulp and stir it in completely, while stirring in enough of the liquid mixture to make a pretty sticky dough. If you used almond milk based yogurt, you will likely need less of the "buttermilk" mixture than if you used a soy or coconut based option.
Transfer the dough to a well floured surface and knead it briefly until it's well consolidated. Pat flat, add a dusting of flour, fold over, pat flat, and repeat this process a couple of times to make layers. Pat the dough to about 1/2 inch in thickness, and use a biscuit or cookie cutter to cut into 3 inch circles.
Transfer the biscuits to a nonstick cookie sheet and bake in a 450 degree F oven for about 10-12 minutes, until completely done - but not burned - on the bottom. Makes about 10 biscuits.
Optional variation: Add 1 tablespoon of coconut sugar to the dry mixture in step 1.