Season the meat with salt and pepper.
In the Dutch oven, heat the oil over high heat until it is almost smoking. Add the meat in batches — not all at once! — and sear on all sides until it is well-browned (not gray). Dump too much meat into the pot at the same time, and you'll overcrowd it; cool the thing down, and you won't get good color.
Sear the meat a little at a time, removing it and setting it aside as it finishes. When all the meat is a nice, dark brown color and has been set aside, add the onions to the pot. Lower the heat to medium-high until the onions are soft and golden brown (about 10 minutes). Sprinkle the flour over them. Continue to cook about 4 to 5 minutes, stirring occasionally. Then, add the red wine. Naturally, you want to scrape up all that really good fond from the bottom of the pot with your wooden spoon. Bring the wine to a boil.
Return the meat to the pot and add the carrots, garlic and bouquet garni. Add just enough water (and 2 big spoonfuls of demi-glace, if you have it) so that the liquid covers the meat by ⅓ — meaning you want a ratio of 3 parts liquid to 2 parts meat. This is a stew, so you want plenty of liquid, even after it cooks down and reduces. Bring to a boil, reduce to a gentle simmer, and let it cook for about 2 hours, or until the meat is tender (break-apart-with-a-fork tender).
You should pay attention to the dish, meaning check it every 15 to 20 minutes, stirring and scraping the bottom of the pot to make sure the meat is not sticking or, God forbid, scorching. You should also skim off any foam, scum or oil collecting on the surface using a large spoon or ladle.
When done, remove and discard the bouquet garni, add the chopped parsley to the pot and serve.