Brown beef. Heat oil in a large, deep frying pan that is big enough to hold the meat. If you don't have a frying pan big enough use a large Dutch oven. Add beef, salt, cumin, and oregano and cook over medium-high heat, stirring occasionally, until beef is browned, about 8 minutes.
Saute veggies. Add poblanos, onion, jalapenos, garlic, and chipotles and continue cooking until veggies begin to soften, about 10 minutes more.
Braise. Add tomatoes and broth, bring to a boil then reduce heat to low, cover and simmer for 30 minutes. Remove lid and continue simmering until beef comes apart when pressed with a fork and sauce is thickened, about an hour and a half more.
Serve. Spoon over rice and top with sour cream and chopped cilantro or serve as tacos.