Rub the garlic and thyme leaves all over the meat. Place the joint in a large dish, drizzle it over the olive oil and rub it all over the meat. Cover and marinate in the refrigerator for 1 to 2 days before cooking. (If you prefer not to marinate the meat before cooking, simply place the garlic / thyme / joint and the oil-rubbed meat on a large roasting pan and proceed to step. 3). Take the meat out of the fridge about an hour before cooking, to bring it to room temperature.
Preheat the oven to 190 ° C / 170 ° C fan / Gas 5.
Preheat a dry skillet until very hot, then brown the meat over high heat until colored on all sides. Place the meat on a large fireproof roasting pan with the garlic halves and thyme sprig and roast for about 45 minutes over medium heat (or until it reaches 45-47 ° C in the center). . Add 10 to 12 minutes for the medium (or until it reaches 55–60 ° C in the center), or add about 20 minutes if you like it cooked through (or until it reaches 65–70 ° C in the center).
Put the meat in a warm pan, cover it with aluminum foil, let it rest for 20 minutes to 40 minutes, before serving.
For the sauce, set the simmering pan on the counter, add the onions to the pan juices, and simmer for about 20 minutes, stirring occasionally, until really soft and caramelized. Add the flour until just combined, then add the red wine, there should be no lumps. Bring to a boil, whisking, then rapidly bubble until the red wine has reduced by half. Add the hot broth, then cook over medium heat for about 8 minutes, stirring occasionally, until it reduces to a thick sauce.
Cut the meat finely and pour the sauce into a warm pitcher. Serve.