Preheat oven to 325 degrees F
In a large dutch oven, melt 2 tablespoons of butter. Add the onions, bacon and carrots sauté until vegetables are slightly golden and soft. Add the garlic, parsley, and thyme, cook for about 2 minutes. Add the tomato paste and mix well with the vegetables. Remove vegetables to a bowl.
Increase heat to medium high and add about 1-2 tablespoons of extra virgin olive oil. Completely dry the beef cubes, season with salt and pepper and brown the beef cubes in batches, adding more olive oil as needed. Reserve browned beef in a bowl. Deglaze the pot with cognac, simmer for about 2-3 minutes.
Return the vegetables and beef to the dutch oven and sprinkle with 2 tablespoons of flour. Set the dutch oven in the preheated oven uncovered for about 5 minutes to brown the flour. Stir gently. Add red wine to barely cover the vegetables and beef. Add the celery stalk and bay leaves. Cover the dutch oven and place in lower third of oven. Adjust oven if needed so that the liquid simmers very slowly for about 3 hours or until beef is tender.
Before serving sauté mushrooms in remaining 2 tablespoons of butter, season with salt and pepper. Boil small red potatoes if using.
To serve, remove bay leaves and celery stalk, mix in mushrooms and potatoes and garnish with chopped parsley.