Combine the beef, celery, carrots, onion, garlic, mushrooms and red wine in a large bowl. Make a sachet by placing the thyme, parsley, bay leaf and peppercorns in the center of a piece of cheesecloth, gather the corners and tie closed with kitchen twine. Add the sachet to the beef and vegetables and marinate in the refrigerator overnight.
Strain the marinated beef and vegetables making sure to reserve the wine. Spread the beef and vegetables on a baking tray separating the beef from the vegetables. Generously season the beef with salt and pepper.
Pour the wine into a saucepan and bring to a boil, skimming the foam off the top as it comes up to a boil. Remove from heat.
Heat canola oil in a heavy bottomed stock pot, working in batches so as to not crowd the pot, sear the beef and cook over medium-high heat until nicely browned on all sides.
Remove the beef from pan and discard all but 1 tablespoon of oil. Render the bacon until crisp and add the celery, carrot, onion, garlic and mushroom; cook until lightly caramelized, about 5-7 minutes.
Deglaze the pan with the rum or brandy and add the browned beef, red wine and chicken stock. Bring to a boil, reduce the heat to low and simmer for about 1 1/2 hours, until the beef becomes tender. Stir the flour into 1/4 cup of water and slowly whisk into the stew. Continue cooking the stew for another 1/2 hour until thick and the beef is very tender.
Prepare the carrots by peeling and slicing them thinly. Place the sliced carrots in a sauté pan and add water to barely cover the carrots, add the butter and lightly season with salt and pepper. Simmer the carrots until tender, about 6 to 8 minutes, garnish with chopped parsley and serve with the beef bourguignon.