Preheat oven to 325°. Pat chuck roast dry with paper towels; very generously season with salt and pepper on all sides.

In a large Dutch oven over medium-high heat, heat oil. Add beef and cook, turning occasionally, until golden brown, 5 to 7 minutes per side. Transfer beef to a large plate.

Reduce heat to medium-low. Add onion and tomato paste and stir until coated. Add wine, scraping bottom of pan to release any brown bits. Bring to a simmer and cook, stirring occasionally, until reduced by about half, about 2 minutes.

Add about half of carrots and potatoes to pot. Place beef on top. Arrange remaining carrots and potatoes around beef. Pour in broth and add thyme.

Cover pot and transfer to oven. Bake pot roast until beef is easily shreddable with a fork, 2 hours to 2 hours 30 minutes. Transfer beef to a cutting board. Using a slotted spoon, transfer vegetables to a plate. Discard thyme.

Return pot to medium heat and bring broth to a simmer, stirring occasionally, until reduced by half, about 10 minutes.

Shred meat with 2 forks. Divide among plates. Serve with vegetables and broth alongside.