In a small bowl, dissolve the yeast in warm water. Let this mixture stand until foamy. In another bowl, combine salt, sugar, oregano, basil, ground pepper and the whole wheat flour.
Make a well in the center of the dry ingredients and pour the yeast mixture and oil into the center. Stir everything with a wooden spoon until a soft, shaggy dough is formed.
Dust a clean surface with a little bit of all-purpose flour. Turn the dough over into the floured surface and knead, adding more all-purpose flour as needed to help with the stickiness of the dough. Once the dough is elastic and smooth (note that whole wheat dough is more sticky than all-purpose flour dough so it is fine if your dough seems to be stickier than usual), shape it into a ball and place it in a bowl. Cover it with a towel and let rise for 1 hour or so, until doubled in size. Meanwhile, make the caramelized onions (instructions below).
Gently deflate the risen dough and place it on a greased 15x 10 inch baking sheet. Pat the dough into a rectangle to take the shape of the pan, and that is about 1/2 inch thick. Cover the pan loosely and let rise for 25 minutes.
Preheat oven to 425 F. Make indentions in the surface of the dough by poking it with your fingers. Brush olive oil all over the dough, sprinkle mozzarella and the caramelized onions. Bake focaccia in the oven for 12-16 minutes or until the top is lightly browned and the cheese has melted. Serve warm.
Heat butter in a medium skillet until bubbly, add the onions and cook over medium heat, tossing frequently. Once the onions are soft and translucent, add the salt and drizzle a little bit of honey. Continue to cook until the onion has caramelized. Turn off heat.