Stir in the olives, parsley, caraway and cumin. Season with salt and pepper.
Heat the oil in a very hot non-stick frying pan.
Pour the mixture into the pan, move the pan to distribute evenly and leave for 7 seconds without stirring.
Tilt the pan and move the cooked egg to the center with a spatula, allowing the uncooked egg to replace the cooked egg. When there is the hint of uncooked egg left, fold the omelette in half and transfer to a warm platter, sprinkle with paprika and tarragon.