Preheat oven to 425°F. Line a baking sheet with parchment paper. In a large bowl, stir together flour, baking powder, and salt. Using a pastry blender, cut in butter, yogurt, and oil until mixture resembles coarse crumbs. Stir in cheese. Make a well in the center of the flour mixture. Add milk all at once. Using a fork, stir just until moistened.
Turn out dough onto a lightly floured surface. Knead dough by folding and gently pressing it just until dough holds together. Pat dough into an 8½ x 4½-inch rectangle. Cut dough lengthwise in half. Cut each half crosswise into four biscuits. Place biscuits, 1 inch apart, on prepared baking sheet.
Bake about 14 minutes or until golden brown. Serve warm. To store: Place any remaining biscuits in an airtight container. Cover and store in the refrigerator for up to 2 days or freeze for up to 2 months.