Wash the large mushrooms well, clean them of stems and set aside (stems can be stored in the freezer for other dishes). Mix the cheeses with the milk to make a mixture and set them aside also.
Cut the pickles and ham into very small cubes and add them to the bowl with the mixture mentioned above. Add dill, salt and pepper. Everything is mixed well with a spoon. Fill the mushrooms with this newly created mixture.
Melt the butter and pour it on the bottom of the tray in which you intend to bake the mushrooms. Sprinkle it with grated cheese.
Bake until golden.