Preheat oven to 400 F.
Line a baking sheet with parchment or foil that has been greased.
Pour the vinegar into the milk and set aside.
In a bowl, combine flours with baking powder, baking soda, spices, and salt. Stir vigorously with a whisk or a fork.
Cut in the shortening with a pastry cutter, fork, or well-floured fingers until the mixture resembles coarse crumbs. Stir in the cheese.
Combine the beaten egg with the milk/vinegar. Make a well in the center of the dry ingredients and add the wet ingredients. Stir just until all ingredients are moistened, being careful not to overmix.
Using a scoop or large spoon, drop about an eighth of the batter onto the baking sheet.
Repeat using the remaining batter.
Check biscuits after 10 minutes. They should be firm and the tops should spring back lightly when touched.
Leave for an additional 2 to 5 minutes to finish baking, if necessary.