Break the eggs in a bowl, and stir with a fork.
Add the milk in the bowl and stir it together with the eggs.
Add the spices in the egg mixture and stir.
Cut the ham in small pieces, and add it in the mixture.
Wash the arugula and add it in the bowl.
Grate the cheese and the add it in the bowl and mix everything together.
Heat up a frying pan and add butter or oil to fry in.
Pour the egg mixture in the frying pan, and fry the omelet on both side until it is golden brown on the surface. Serve the omelet warm.