In a large bowl, dissolve yeast in 1/2 cup warm water. Add the oil, honey, salt, seasonings, egg, whole wheat flour and remaining water. Beat until smooth. Stir in enough all-purpose flour to form a soft dough.
Turn onto a floured surface; knead until smooth and elastic, 6-8 minutes. Place in a greased bowl, turning once to grease top. Cover and let rise in a warm place until doubled, about 1 hour.
Punch dough down. Turn onto a lightly floured surface; divide into six portions. Divide each into 24 pieces. Shape each into a 1-in. ball; place three balls in each greased muffin cup. Cover and let rise until doubled, 20-25 minutes.
Bake at 375° for 12-15 minutes or until tops are golden brown. Remove from pans to wire racks. Yield: 4 dozen.