Pat the beef chuck cubes dry with paper towels. Season generously with salt and pepper. Heat 2 tablespoons of olive oil in a large Dutch oven over medium-high heat until shimmering.
Working in batches to avoid overcrowding, sear the beef cubes on all sides until deeply browned, about 3-4 minutes per batch. Transfer to a plate and set aside.
In the same pot, add the remaining tablespoon of olive oil. Add onions and sauté until translucent, about 5 minutes. Add garlic and cook until fragrant, about 30 seconds.
Stir in tomato paste and cook for 2 minutes until it darkens slightly.
Pour in the red wine, scraping the bottom of the pot with a wooden spoon to release all the flavorful brown bits. Simmer for 3-4 minutes until the wine reduces by half.
Return the beef to the pot along with any accumulated juices. Add beef broth, bay leaves, rosemary, and thyme. Bring to a boil, then reduce heat to maintain a gentle simmer.
Cover and cook for 1 hour and 30 minutes, or until beef is nearly tender.
Add carrots, parsnips, butternut squash, and mushrooms to the pot. Continue simmering, covered, for another 30 minutes or until vegetables are tender but not mushy.
In a small bowl, whisk together flour and 1/4 cup of cold water until smooth. Gradually stir this mixture into the stew and simmer for 10 minutes until thickened.
Add Worcestershire sauce and balsamic vinegar. Taste and adjust seasoning with salt and pepper.
Remove bay leaves and herb stems before serving. Garnish with fresh chopped parsley.