Peel the knob celery and carrot, then cut into small dice. Cook covered in 2tablespoons of the butter for about 10 minutes. Every 3 minutes or so add 1teaspoon of water, to make enough steam for the cooking.
After the 10 minutes add the chopped cauliflower and mushrooms; cook covered for another 10 minutes. Mushrooms will probably release enough liquid so you don’t have to add more water.
Crumble stale rolls and soak them in milk. Squeeze when soft. Add eggs and mix. Mix with the flour and finally add the cooked vegetable mixture. Add salt and adjust to taste.
Bring 3quarts of water to a boil. Make Ping-pong-ball-sized dumplings and drop them into the water. Cook them for 10 to 15 minutes.
Melt remaining 2tablespoons butter, and cook the drained dumplings in melted butter for a few minutes.