In a large skillet, heat the olive oil over medium-high heat. Season the beef chuck roast with salt, pepper, curry powder, and ground ginger. Sear the roast on all sides until browned, about 4-5 minutes per side.
Transfer the seared beef to a slow cooker. Pour in the coconut milk, beef broth, soy sauce, and lime juice. Stir to combine.
Add the sliced bell pepper, carrots, onion, and minced garlic on top of the beef.
Cover and cook on low for 8 hours or on high for 4 hours, until the beef is tender and easily shreds with a fork.
Once cooked, remove the beef from the slow cooker and shred it using two forks. Return the shredded beef to the slow cooker and stir to combine with the sauce and vegetables.
Serve the coconut curry shredded beef over cooked rice and garnish with fresh cilantro.