In wok with oil, stir fry onions and garlic for a few minutes. Add bell peppers and bacon and continue frying for a minute.
Add black pepper, soy sauce, ketchup and sesame oil and mix well. Add mushrooms, fry and then let it simmer for about 3 minutes for the water to come out. Remove from heat and set aside this filling for the omelet.
For the first omelet, beat 3 eggs in a bowl. Add 1/2 tsp salt and 1 tbsp water.
Place a flat stainless-steel pan over medium heat. Sprinkle drops of water into it and see how it evaporates. Pan is ready when water form droplets rolling freely on the pan.
Add 1 tbsp butter and let it melt and sizzle. When sizzling stops, add beaten egg.
After about 1 minute, begin scrapping the edges of the egg. When egg edges solidify, scrap it towards the center, tip and allow the egg liquid on top to flow into the exposed edge. Repeat around the edges until minimum liquid remains on top.
Sprinkle 1/4 cup of shredded cheese on top of the egg. When cheese is melted, lift the pan up and shake it horizontally to see movement of the omelet and place back on the heat. Repeat this several times.
When omelet is moving quite freely, Add several spoonsful of the filling on half of the omelet. Using a spatula, flip the other side of the omelet to cover it. Press down on the omelet and let it cook for about 30 seconds. Use a large spatula to remove it intact onto a serving plate.
Repeat with additional omelets until eggs and/or filling is used up.