Combine wheat and barley flour with nutmeg, garlic powder, and tarragon. Cut in butter with a pastry blender. Stir in grated cheese. Make a well in the center and pour in the buttermilk. Stir until just mixed and then squash together by hand into a ball. Let sit a room temperature for 12-24 hours.
Flatten dough a bit and sprinkle baking powder, baking soda, and salt over the top. Knead gently into the dough 10 times.
Roll out into a circle and cut into 8 pieces like you would a pie. Or you can use a biscuit cutter. Brush with buttermilk. Let rest for 10 minutes.