Heat oil in a large skillet over medium-high; brown beef on all sides in batches, about 3-4 minutes per batch. Transfer to slow cooker.
Sauté onion and jalapeño in same skillet about 5 minutes until softened; add garlic and cook another minute. Transfer to cooker.
Add chipotles with adobo, tomatoes, pinto beans, kidney beans, broth, chili powder, cumin, cocoa, oregano, salt, and pepper; stir well.
Cover; cook on LOW 8-10 hours or HIGH 5-6 hours until beef is very tender and shreds easily with a fork.
Stir well, breaking up larger beef pieces; adjust seasoning to taste, adding more adobo for heat if desired.
Serve hot topped with sour cream, Monterey Jack, and green onions.