Boil up plenty of salted water. Clean and wash the broccoli and cut it into florets. Dab fillet dry and cut into 8 medallions. Wash the thyme. Wrap each medallion with thyme stalks if necessary and tie up with kitchen string (or pluck thyme leaves from 4 stalks).
Cook the spaetzle in boiling water for about 15 minutes (see package instructions). Heat the oil in a pan. Fry the medallions on each side. Fry over medium heat for 5-6 minutes.
Season with salt and pepper.
Add the broccoli to the spaetzle after about 10 minutes. Bring to the boil again and cook for about 5 minutes. Remove the meat and keep warm. Dissolve the meat with 1⁄8 l water and red wine. Stir in broth and thyme and let it boil down for about 5 minutes.
Thicken the sauce and season to taste.
Drain the spaetzle and broccoli. Mix with butter and nuts, season. Serve with meat and sauce.