Peel and wash the carrots and cut them in half lengthwise. Celery clean, wash. Cut carrots and celery into slices. Peel onions, chop coarsely. Wash thyme, shake dry. Dab goulash dry.
Heat the oil in a casserole dish. Brown the meat in it in portions until brown. Season with salt and pepper. Stir-fry carrots, celery and onion for about 7 minutes. Add the whole goulash again.
Add tomato paste and sweat briefly. Deglaze with tomatoes, juice and stock, bring to the boil. Add thyme and laurel. Season well with salt, pepper and 1 tablespoon of sugar. Cover and stew at medium heat for about 2 1⁄2 hours until the goulash falls apart easily.
For the puree, peel and wash the potatoes, cover and cook in salted water for about 20 minutes. Meanwhile, for the Gremolata, wash parsley, shake dry, pluck off leaves and chop finely. Peel garlic and also chop finely.
Mix parsley and garlic with lemon peel.
Heat milk and butter in a pot. Drain the potatoes and let them evaporate briefly. Add milk mixture and mash everything. Season to taste with salt and nutmeg. Season stew to taste, remove thyme twigs and bay leaves if necessary.
Serve the stew with mashed potatoes. Sprinkle with gremolata.