Pat the beef chuck roast dry with paper towels and season all sides with salt and black pepper.
Heat olive oil in a large skillet over medium-high heat. Sear the beef roast on all sides until browned, about 3-4 minutes per side. Remove and set aside.
Place the sliced onion and minced garlic in the bottom of the slow cooker.
Add the seared beef roast on top of the onions and garlic.
Pour the diced tomatoes with green chilies and beef broth over the roast.
Sprinkle chili powder, ground cumin, smoked paprika, and dried oregano evenly over the roast and liquid.
Add the sliced green bell pepper, red bell pepper, and jalapeño pepper around the roast.
Cover and cook on low for 8 hours, or until the beef is tender and easily shredded.
Once cooked, remove the beef roast from the slow cooker and shred it using two forks.
Return the shredded beef to the slow cooker and stir to combine with the juices and vegetables.
Stir in the fresh cilantro and lime juice just before serving.
Serve hot with warm tortillas, rice, or your favorite Mexican side dishes.