Heat a large Dutch oven over medium-high heat; add a tablespoon of oil. Season meat well and brown in hot oil in 2 batches, adding more oil as necessary.
In a saucepan, heat ancho chilies in stock and simmer to soften. Pure in a food processor and reserve.
Add a little more oil to the Dutch oven and reduce heat to medium. Add onions, garlic, salt, pepper and spices; stir to combine and cook partially covered to soften, 6-7 minutes. Add tomato paste and stir 1 minute; add wine and reduce by half. Add coffee, chili pure, honey, tomatoes and reserved beef. Bring to a simmer, cover and slow cook 2-2 1/2 hours until very tender.
Shred meat and return to sauce; let cool and skim fat. Reheat beef over low heat while you prepare the pickled onions.
Combine the lime juice with honey or sugar, salt and coriander. Toss with onions, season with pepper. Let stand 1 hour.
Serve meat with bread or tortillas, lots of pickled onions and a few sprigs of green.