Cut the ham and onion into cubes and grate the cheese.
Heat the oil in the pan and fry the onions until translucent; Add the ham and let it become slightly crispy.
Mix the eggs carefully with the milk with a whisk. Add to the onions and ham in the pan. Let it rest for a moment and then turn it two or three times. Season with salt and pepper.
When the scrambled eggs have set, fold in the cheese. Then wait a little longer until the cheese has turned golden brown.
If there is still too much liquid (water) in the pan from the cheese, simply continue to simmer on a low level until the water has evaporated.