Cut away as much visible fat as possible from the beef ribs and discard.(see notes) Season the beef with salt and pepper and brown over high heat in 1 tablespoon of olive oil in a heavy cast iron pan or pot (casserole), remove from the pan and set aside till needed.
Preheat the oven to 150C/300F.
To the same pan add the he bacon lardons until they render fat, remove with a slotted spoon to the same bowl as the beef.
Now add chopped onion to the pan and cook over low heat for 5-7 minutes until tender and translucent, then add minced garlic and cook for 1 minute stirring constantly to prevent garlic from burning or it will turn bitter.
Sprinkle the flour all over the onions and garlic and stir until the flour and the fat in the pan turn into a paste, continue cooking for a few seconds, then slowly stir in the red wine while scraping the bottom of the pan to release the brown bits into the sauce. Add the beef stock and bring to a simmer, now return the beef short ribs and bacon lardons to the pan making sure the meaty parts of the ribs are submerged in the liquid, place the bouquet garni into the centre. The beef should be mostly covered by the sauce. If your pan is too wide and the liquid is too low, add more water or beef stock. Cover with a lid and put in the oven for 1.5 hours.
Take the beef out of the oven and check, the liquid should remain at the same level. If not, add some water, then scatter the mushrooms and the carrots around the beef, cover with a lid and cook for 1 hour longer. Now take out of the oven and take the lid off. The liquid should reduce and thicken and beef should be tender and falling off the bones. If that is not the case, put back in the oven for 30 minutes longer uncovered.
Serve sprinkled with additional chopped parsley over mashed potatoes.