Make a stock of chopped onions, allspice, bay leaves and water for 15 minutes.
Add the peeled and diced potatoes and cook for about 15-20 minutes. Remove allspice and bay leaves. Pour off half of the liquid and replace with the warmed milk. Add the butter and briefly bring to the boil again.
Take the pot off the stove and roughly chop the potatoes with a masher. Finally stir in the finely chopped parsley and dill.