Pat the beef chuck cubes dry with paper towels. In a large bowl, toss the beef with flour, 1 teaspoon salt, and 1/2 teaspoon black pepper until evenly coated.

Heat 1 tablespoon of olive oil in a large Dutch oven or heavy-bottomed pot over medium-high heat. Sear the beef in batches, making sure not to overcrowd the pot, until browned on all sides. This will take about 3-4 minutes per batch. Remove browned beef to a plate and set aside.

Add the remaining 1 tablespoon of olive oil to the pot. Reduce heat to medium. Add chopped onion and sauté until softened, about 5-7 minutes. Add minced garlic and cook for another minute until fragrant.

Stir in the tomato paste and cook for 1 minute, stirring constantly, to deepen its flavor. Pour in the red wine (if using) and scrape the bottom of the pot with a wooden spoon to deglaze, loosening any browned bits. Let the wine simmer for 2-3 minutes, reducing slightly.

Return the seared beef to the pot. Add the beef broth, dried thyme, dried rosemary, bay leaves, and Worcestershire sauce. Stir to combine. Bring the liquid to a gentle simmer.

Reduce heat to low, cover the pot, and simmer for 1.5 hours. The beef should start to become tender.

After 1.5 hours, add the carrots, celery, and potatoes to the pot. If using mushrooms, add them now as well. Stir gently to combine.

Continue to simmer, covered, for another 45-60 minutes, or until the vegetables are fork-tender and the beef is fall-apart tender.

Taste the stew and adjust seasoning with additional salt and pepper if needed. If the stew is too thin, you can uncover it and simmer for the last 15-20 minutes to allow it to reduce and thicken slightly. Remove bay leaves before serving.

Ladle the hearty beef stew into bowls. Garnish with fresh chopped parsley, if desired. Serve hot with crusty bread or over mashed potatoes.