1. Pat the beef chuck roast completely dry with paper towels. Season generously with salt and freshly ground black pepper.

2. Heat 1 tablespoon olive oil in a large Dutch oven over medium-high heat. Sear the beef for 4-5 minutes per side until deeply browned. Remove and set aside.

3. Lower heat to medium. Add remaining 1 tablespoon olive oil, chopped onion, and carrots. Cook for 5-7 minutes until onions soften. Stir in garlic and cook for 1 minute.

4. Sprinkle 2 tablespoons of flour over vegetables. Stir and cook for 1 minute. Add tomato paste and cook another minute.

5. Pour in beef broth gradually, scraping browned bits. Stir in thyme and bay leaf. Bring to a simmer.

6. Return seared beef to pot, mostly submerged in liquid. Cover and transfer to preheated oven at 300°F (150°C).

7. Braise for 3 to 3.5 hours until beef is fork-tender and shreds easily.

8. During final 30-45 minutes, prepare mashed potatoes: place potatoes in pot, cover with cold water, add salt, boil then simmer until tender. Drain thoroughly.

9. Mash potatoes. Add warm milk or cream and softened butter. Mash until fluffy. Season with salt and pepper.

10. Remove beef and discard bay leaf. For thicker gravy, whisk remaining 2 tablespoons flour with 1/4 cup cold water and add to simmering pot liquid. Stir until thickened.

11. Shred beef with two forks and return to pot, mixing with gravy.

12. Serve hot over mashed potatoes. Garnish with chopped chives if desired.