In a mixing bowl, dissolve yeast in water. Stir in honey; let stand for 5 minutes. Add the potatoes, buttermilk, butter, thyme and salt. Add the egg, whole wheat flour and 1 cup of all-purpose flour; beat on medium speed to form a soft dough. Stir in enough remaining all-purpose flour to from a stiff dough. Turn onto a floured surface; knead until smooth and elastic, about 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 three portions; divide each into 18 pieces. Shape each into a ball; place three balls each in greased muffin cups. Cover and let rise until doubled, about 25 minutes. For the glaze, combine egg and milk; brush over rolls. Bake at 400° for 15-18 minutes or until golden brown. Remove from pans to wire racks to cool.
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