In a large enameled Dutch oven, heat 1 tablespoon of the vegetable oil and 1 tablespoon of the butter over medium heat until hot but not smoking. Add the bacon and saute over medium heat for 5 minutes. Add the sliced onion and cook, stirring, until wilted, 3 minutes. Finally, add the garlic, cook 1 minute longer, and remove from the heat.
Heat the remaining 1 tablespoon oil and 1 tablespoon butter in a large skillet over high heat until the foam subside. Add half the meat and saute until browned on all sides, about 5 minutes. Transfer the browned meat to the Dutch oven and saute the second batch.
In the same skillet, saute the pearl onions and mushrooms until lightly browned, about 5 minutes. Set aside.
Sprinkle the flour over the meat in the Dutch oven and season with salt and pepper. Stir the meat and flour with a wooden spoon over low heat for 1 minute. Add the wine, Cognac, and bouquet garni. Bring to a simmer, stirring frequently. Do not boil; even the briefest boiling would result in leathery and tough meat. Simmer the stew, covered, over very low heat until the meat is very tender, 2 hours; skim the fat and foam from the surface occasionally.
Add the mushrooms and pearl onions and simmer for another 30 minutes. The meat and vegetables should be very tender. Remove the bouquet garni. Taste and adjust the seasoning. Sprinkle with the parsley and serve.