Peel and wash turnips and potatoes. Cut both into cubes of the same size. Bring to the boil in plenty of water with salt and cook over medium heat for about 25 minutes. Peel and finely chop onions and garlic.
Heat the oil in a large frying pan. Fry the minced meat, onion and garlic until crumbly. Add tomato paste and fry briefly. Pour in broth, bring to the boil briefly. Season minced meat sauce with salt, pepper, paprika and thyme.
Put the chopped sauce aside. Drain the turnip and potato vegetables, collecting the cooking liquid. Warm the milk. Mash the vegetables with a potato masher. Stir in 100 ml cooking water and milk.
Season the puree with salt and pepper. Finely chop the slices of bread (preferably in a universal chopper). Put the chopped sauce in a large casserole dish. Spread the puree on top. Put butter as flakes on top, sprinkle with bread crumbs and bake in a preheated oven (electric range: 225 °C/ gas: level 4-5) for about 25 minutes.
Serve garnished with fresh thyme as desired.