Start by trimming any excess fat from the chuck roast. This will help prevent the dish from becoming greasy.
In a large mixing bowl, combine the low-sodium soy sauce, beef broth, beef bouillon cubes, garlic powder, onion powder, dried rosemary, dried thyme, and black pepper. Stir until the bouillon cubes dissolve.
Place the chuck roast in the slow cooker and pour the broth mixture over the top, ensuring the beef is well-coated.
Cover the slow cooker and cook on low for 8 hours or high for 4 hours. The longer it cooks, the more tender the meat will become.
Once the cooking time is up, carefully remove the roast from the slow cooker and place it on a cutting board. Use two forks to shred the beef into bite-sized pieces.
In a skillet over medium heat, melt a little butter. Split the hoagie rolls and place them cut-side down in the skillet. Toast until golden brown and crispy.
Fill each toasted hoagie roll with shredded beef and top with a slice of provolone cheese. You can place the sandwiches under the broiler for a minute to melt the cheese further if desired.
Serve your Slow Cooker French Dip sandwiches with a small bowl of the cooking broth for dipping. Enjoy every savory bite!