Preheat an 8-qt. Dutch oven over medium heat. Add the bacon and cook until crispy. Remove the bacon from the pan and reserve.
Season the meat with salt and freshly ground black pepper. Using the bacon fat that remains in the pan, sear the meat over medium heat until brown on all sides. Add additional vegetable oil, as needed. Remove the meat from the pan and reserve.
Add the onions and sauté for 3 - 4 minutes or until tender. Add the garlic, thyme, parsley stems and bay leaves and sauté for 1 - 2 minutes, stirring constantly. Add the crispy bacon, tomato paste, beef stock, red wine and cognac and bring the mixture to a boil.
Return the meat to the pan and bring all to a very slow simmer. Place the cover on top of the pot and continue to cook at a low simmer for 2 1/2 - 3 hours or until the meat is very tender.
During the last 30 minutes of cooking, preheat the oven to 400°F/205°C.
Toss the mushrooms with 2 Tbsp. of olive oil and season with salt and pepper. Roast the mushrooms on a baking sheet for 10 - 15 minutes or until golden.
Add the pearl onions to the beef stew.
Place the sweet potatoes in a large pot of water, and bring to a boil. Reduce the heat and let the potatoes simmer for 15 - 20 minutes or until tender.
Add the green beans and peas to the pot and cook for 2 minutes. Drain the pot and set the vegetable mixture aside.
In a small bowl, create a beurre manie by combining the butter and flour. Whisk the beurre manie into the stew and allow the stew to return to a boil. Continue to cook until the sauce is thick. (Add additional beurre manie as needed to thicken).
Remove bay leaves and parsley stems from the stew and discard.
Add the mushrooms, potatoes, beans and peas to the stew. Season to taste with salt and pepper.
Mix in the chopped parsley and serve hot with crusty bread.