Whisk the eggs with the water and salt and pepper. Water helps bond the egg, so the omelet will fold more easily.
Put 3/4 (15g) of the butter and 1/2 (ie. a dash) of the olive oil in a good non-stick 20cm to 30cm frying pan. Heat till the butter bubbles. Mixing the oil with butter makes the mixture spread out, and mushrooms taste better cooked in butter.
Put the mushroom, onion and bacon (and potato, if using) in the frying pan. Cook until the onion starts to brown (and stir to ensure the mushroom soaks & bacon cooks). Remove from the pan.
Put 1/4 (5g) of the butter and another dash of the olive oil in the pan. Again heat until it bubbles. Make sure it covers the base of the frying pan (by tipping & tilting the frying pan). Put the whisked egg in the frying pan, and make sure that it covers the base of the frying pan (by tipping & tilting again).
Immediately put the cooked bacon, mushrooms & onions on one half of the omelet - whichever half looks like it might cook the slowest. Lay the cheese on top of the bacon, mushrooms & onions.
Test lifting the other side of the omelet. When it is cooked enough to be solid enough to lift, lift it with one or two spatulas to cover the other half of the omelet. You can lift with one spatula and jerk the frying pan, but it might be easier to use two spatulas.
Leave the omelet to cook on a lowish heat for another minute - so the cheese will completely melt through. Then serve.