Heat 4 tablespoons olive oil in a deep frying pan. Add onions and cook slowly, stirring occasionally, 30 minutes or until soft and golden.
Add the potatoes to the onions and turn up the heat a bit. Cook until the potatoes are soft but not crispy, breaking them up with a spatula and stirring frequently. When it is all a brown mush, take off the heat and let cool slightly.
Beat the eggs in a bowl and add the potato/onion mix. Season with salt and pepper.
Heat a tablespoon of olive oil in a small non-stick frypan over medium heat and add 1/6 of the mixture. Cook 2 minutes then invert the omelette onto a plate. Slide it back in the frypan to cook the other side a minute or two then remove to a plate and keep warm. Repeat with the rest of the mixture to make 6 omelettes.