Cut the roast beef into even slices. Season both sides with salt and pepper, then sprinkle with chopped thyme.
Finely chop the onions and dice the raw ham.
Heat lard in a large braising pot over medium-high heat. Add the meat slices, onions, and diced ham. Cook, stirring occasionally, until the meat is browned and the onions are softened, roughly 5-7 minutes.
Dust everything with flour and stir well to coat. Add the grated garlic, the halved carrot, and bay leaf. Cook for 2-3 minutes.
Pour the Burgundy wine over everything. Bring to a simmer, then reduce heat to medium-low. Cover and braise for 30 minutes until the beef is tender. If too much liquid reduces, add water to maintain sauce level.
Transfer to a serving dish, sprinkle generously with parsley, and serve with pasta or boiled potatoes.