Cut the savoy cabbage into strips and wash. Don`t use the harder parts of the head.
Heat the oil in a pan and fill it with savoy cabbage. Sear it and add a handful of savoy cabbage from time to time until it is completely in the pan. Let simmer for another 5-10 minutes over medium heat. If the savoy cabbage threatens to burn, deglaze with a little water and reduce the heat. Salt lightly.
In the meantime, whisk the eggs with the milk and season with salt, pepper and nutmeg. Pour the mixture over the savoy cabbage into the pan and let it set while stirring occasionally.