Break the eggs into a small bowl and scramble them. Mix in thyme, cayenne, and some pepper.

Heat the oil in a frying pan and add the egg mixture, making an even layer.

Sprinkle the rest of the ingredients over the egg and let it cook for a minute or two.

Using a spatula, flip half of the omelette onto the other half and continue cooking for another minute or two until fully cooked. Serve.