Preheat oven to 400°F. In a mixing bowl (or in the bowl of a food processor) stir together the flours, baking powder and salt; add the butter and oil and pulse or stir with a wire whisk or fork until crumbly. If you’re using a food processor, transfer the mixture to a bowl. Toss in the grated cheese.
Add the milk and stir gently until the dough begins to come together. For wedge-shaped biscuits, pat the dough into a circle that is about 1” thick on a cookie sheet. Cut the circle into 8 wedges with a knife or pastry cutter and separate them so that they are at least an inch apart on the sheet. For round biscuits, pat the dough about 1” thick and cut it into rounds with a biscuit cutter, glass rim or open end of a can, gently rerolling the scraps only once to get as many biscuits as possible.
Bake for about 20 minutes, until golden. Serve warm. Wrap well and freeze any you don’t eat the same day.