Heat the oven to 400 degrees F. Spread parchment paper on a large baking sheet and sprinkle with 1 tablespoon whole-wheat flour. Set aside.
Mix together the all-purpose flour, baking powder, sugar, salt and 1 cup whole-wheat flour in a large bowl, using a fork. Cut or rub in the butter into the flour mixture, with a pastry blender or your fingertips, until the mixture resembles coarse sand with a few pea-sized butter pieces remaining. Add the onions, cheese and thyme and toss gently.
Whisk together the egg and milk in a small bowl; add to the flour mixture and stir gently with a wooden spoon just until mixed (do not overmix). The dough will be sticky.
Turn the dough onto the prepared baking sheet. Sprinkle with the remaining tablespoon whole-wheat flour. Using a serrated knife that's been coated with cooking spray, divide the dough in half and shape into two 5-inch circles. Score each circle into 6 wedges with the knife.
Bake until firm to the touch, 20 to 25 minutes. Cut each circle into 6 wedges using the scored lines and serve.