Prepare the pasta in boiling salted water according to the instructions on the packet. Peel garlic and chop finely. Peel and finely dice the onion. Wash thyme, shake dry and chop finely except for 5 stems.
Cut the fillet into 8-9 medallions, press a little flatter. Season with salt. Heat oil in a pan. Sauté the meat in it for about 2 minutes on each side. Finally add 3 stalks of thyme and fry briefly.
Remove medallions from the pan, season with pepper and keep warm.
Drain the pasta. Collect 200 ml pasta water. Briefly fry the onion, garlic and chopped thyme in hot frying fat until transparent. Add the chopped tomatoes, stock and pasta water and simmer over medium heat for about 10 minutes.
In the meantime, cut the broccoli florets from the stalk, possibly halve them and cook in boiling salted water for 4-5 minutes. Drain and rinse with cold water. Season sauce with salt and pepper. Add pasta and broccoli and stir in.
Place in an ovenproof dish (approx. 16 x 25 cm) and place medallions in the middle of it. Grate the cheese finely and sprinkle on the casserole. Gratinate under the hot grill for 4-5 minutes. Garnish the casserole with the remaining thyme.