Trim any excess fat from the beef chuck roast and cut it into 1-inch cubes, then place them into the slow cooker.
Peel and dice the russet potato into 1-inch pieces, and slice the carrots into half-inch rounds.
Add the diced potatoes, sliced carrots, and trimmed green beans to the slow cooker with the beef.
In a small mixing bowl, whisk together the beef broth, tomato paste, garlic powder, onion powder, dried thyme, sea salt, and black pepper until well combined.
Pour the broth mixture over the beef and vegetables, stirring gently to ensure all ingredients are lightly coated.
Cover the slow cooker and cook on the low setting for 7 to 8 hours, or on high for 4 hours, until the beef is fork-tender.
Give the stew a final stir to incorporate the thickened juices before serving warm.