Mix the cream cheese with the coriander in a bowl until soft and spreadable adding salt and pepper to taste.
Heat one-quarter of the butter in a well-seasoned omelette pan or non-stick frying pan over medium-high heat. When the butter is hot and bubbling, swirl it around in the pan.
Just before the butter begins to brown, beat 2 of the eggs and pour into pan. Lower the heat.
After 10 seconds or so, the omelette will coagulate. Push the omelette to one side of the pan with a spoon or spatula, and let the raw egg run over the cleared frying pan. Repeat this one more time, then take the frying pan off the heat.
Dollop one quarter of the herbed cream cheese along the middle of the omelette from one side to the other.
Season the omelette with additional salt and pepper to taste. If it has not completely set, place the pan over medium heat for a half minute longer.
When the omelette is set, slide it from the pan onto a plate so that the omelette rolls up and the herbed cream cheese runs along the length of the roll. Serve it right away.
Make three more omelettes the same way, making sure the pan and butter get good and hot before adding the beaten eggs. Serve each one as soon as it is cooked.