Wash the rabbit legs, pat dry and place in a dish in opposite directions. Peel the carrot and onion and cut into pieces over the meat.
Put red wine, vinegar, spices and thyme in a saucepan and bring to a boil. Pour the cooled stock over the legs and cover and marinate for at least a day.
Remove the meat, drain well and rub with salt and pepper. Heat the oil in a casserole and fry the legs all over. Lift the vegetables out of the marinade with a slotted spoon, drain well and add to the meat with the tomato paste. Fry with, then add the stock and marinade and cover and let simmer for about an hour over low heat.
In the meantime, put the flour, salt, eggs and oil in a bowl for the spaetzle dough and work through with the dough hook of a hand mixer until the dough starts to bubble. If the dough is too firm, add one to two tablespoons of water.
Heat plenty of water in a large saucepan and scrape the spaetzle from a moistened wooden board with a knife into the boiling water or use a spaetzle slicer. As soon as the spaetzle floats on the surface, lift it out with a slotted spoon and pour it into the cold water.
Remove the rabbit legs from the stew, remove the meat from the bone and keep warm. Let the stewing liquid boil down by about half, then pass through a fine sieve and season again if necessary. Put the meat back into the sauce and briefly heat it up.
Briefly toss the spaetzle in hot butter and season with salt and a touch of freshly grated nutmeg. Place the spaetzle and braised rabbit in a bowl and serve.