Mix together the yeast and water and let it stand in a warm place for five minutes until the yeast starts to multiply.
Add to the yeast the nondairy milk, oil, shortening, sugar, flaxmeal mixture, and mix till well blended.
Add the bread flour and white whole wheat flour.
Knead until well integrated and dough forms in a smooth ball, about 10 minutes on low speed in a stand mixer, or by hand. The dough will be slightly moist but not sticky.
Now place in an oiled bowl, turning once to coat with oil. Cover with a kitchen napkin and set aside to rise about 1 ½ hours.
Punch down the dough, then divide it into 18 pieces. Roll each into a ball and place on a greased baking sheet, about 2 inches apart.
Brush the rolls with some olive oil and let them sit in a warm place for about 1 hour until they are approximately double in size.
Make a wash with 1 tablespoon olive oil and 1 tablespoon soy milk. Brush the tops of the pompoms with this wash: it will give them a beautiful golden-brown color when they are baked.
Bake in a preheated 425-degree oven for about 15 minutes, until the crust is golden-brown. Eat warm. To reheat, put in a 350-degree oven for about 3 minutes (I usually preheat them directly on the rack, but be careful as ignoring them for just a little longer might burn the bottom!).