Place crushed ginger and garlic in a 1 gallon size plastic locking bag.
Add soy sauce, sweetener and oil to bag, seal and shake well.
Clean portabello mushrooms by wiping off dirt with a clean damp cloth. Cut off stem end of mushrooms.
Place mushrooms in bag with soy mixture, reseal and let stand about 15 minutes. Heat nonstick skillet on range on medium high heat.
Remove mushrooms from bag and place cap side down in hot skillet. Cook 2 to 3 minutes and turn mushrooms. If the skillet is dry add some of the soy sauce from the bag.
Continue cooking until the skillet is almost dry and sauce caramelizes on mushrooms. Remove skillet from heat.
Optional: If you do not like the taste of raw onions, you may remove mushrooms from skillet and set aside. Add 1-2 tablespoons of canola oil to skillet on medium heat and sweat sliced onions until translucent and caramelized.
To assemble the sandwich, spread mayonnaise on each half of the kaiser roll.
Place 1 lettuce leaf, cut to fit the bun on one half. Place cheese slice on top of lettuce and then 1 tomato slice on top of the cheese.
On the other half of the bun, place 1 portabella mushroom and either the cooked or raw onion slice on top of the mushroom. Put the two halves of the buns together and enjoy.