Peel and dice the potatoes. Cook in boiling salted water for about 15 minutes.
Wash and clean the cabbage, cut into strips and blanch in the salted water for 3-4 minutes. Drain both well.
Pour the milk onto the hot potatoes.
Add the butter.
Season with salt and pepper.
Mash to a fine puree.
Mix the cabbage with the mashed potatoes.
Pour the potato and cabbage mixture into a hot pan with the oil. Press evenly flat and brown for about 4 minutes.
Fry, turning occasionally, for another 3-4 minutes until golden brown.