In a large bowl, stir together the all-purpose flour, and whole wheat flour, baking powder, baking soda, salt and 2 Tbsp of the cheese In small skillet, heat 1 Tbsp of the oil over moderate heat. Add the basil and cook for 1 minutes; transfer to a small bowl and cool slightly.
Stir in the yogurt, milk, and remaining 1 Tbsp of oil.
Add the basil mixture to the dry ingredients and stir until just combined.
Place the dough on a well-floured surface. Using a lightly floured rolling pin, roll out the dough until 1/2" thick.
Using a 2 1/4" biscuit cutter or glass, cut out rounds, gently rerolling the scraps, to form 12 biscuits.
Place the biscuits on an ungreased baking sheet, spacing them 1" apart. Sprinkle with the remaining 2 tsp of cheese and bake for 12 to 15 minutes or until golden.