Pat the beef chuck roast dry with paper towels and season all sides with kosher salt and freshly ground black pepper.
Heat the olive oil in a large skillet over medium-high heat until shimmering.
Add the beef roast to the skillet and sear each side for about 3-4 minutes until browned. Remove the roast and set aside.
In a small bowl, combine the minced garlic and chopped fresh rosemary.
Place the sliced onion, carrots, and celery in the bottom of the slow cooker.
Place the seared beef roast on top of the vegetables in the slow cooker.
Spread the garlic and rosemary mixture evenly over the top of the roast.
In a separate bowl, whisk together the beef broth and tomato paste until smooth, then pour over the roast and vegetables.
Cover the slow cooker and cook on low for 8 hours, or until the beef is tender and easily shredded with a fork.
Once cooked, remove the beef from the slow cooker and let it rest for 10 minutes before slicing against the grain.
Serve the sliced roast beef with the cooked vegetables and spoon some of the cooking liquid over the top.