Heat 5 tablespoons of the oil in a 25cm/10in frying pan and fry the pepper strips, stirring from time to time, until the edges of the strips are caramelised, this should take about 10 minutes.
Add the garlic and fry gently until it is cooked but not burnt. Add the vinegar, and cook until evaporated. Remove from the heat and set aside, leaving the peppers in the pan.
Beat the eggs in a bowl and season with salt and pepper.
Return the frying pan to the heat, add the remaining oil and pour in the egg mixture. Cook, stirring a little with a spatula, until there is a crust on the underside, this should take about five minutes.
Cover the pan with large plate or the lid of a large saucepan, and quickly turn it upside down to invert the omelette. Slide it back into the frying pan, crust-side up. Cook for a further 5 minutes, until the other side has browned. Cut into wedges and serve hot or cold with salad.