Wipe fresh chanterelles with a napkin (do not wash!), Defrost frozen ones and dry with a napkin. Break the eggs into a bowl, add greens, salt and pepper, lightly beat with a fork.
Heat two-thirds of the oil in a large frying pan, fry the chanterelles (3 minutes). Pour in the egg mixture and level with the flat side of a fork. Once the omelette has set, place it on a plate.
Heat the remaining oil in a skillet. Cover the omelette with another plate, flip and return to the skillet to brown the other side (1 minute). Serve cut into portions.