Preheat broiler and position rack as close to the broiler heat source. Line the bottom of a broiling pan with aluminum foil (this will catch any juices from the peppers). Place poblano peppers on top of the broiling pan. Place under the broiler. Let cook until peppers’ skin is blackened, turning peppers with tongs so they blacken on all sides, approximately 10 to 15 minutes.
Place peppers in a large plastic bag and loosely seal for 30 minutes. Remove and discard as much of the blackened skin as possible along with the stems and seeds. Use your hands. Don't rinse peppers under water, you'll rinse away flavor. If you want your chili to be hotter, leave in some of the seeds (source of the peppers’ heat). Coarsely chop peppers and set aside.
Repeat this roasting process for the hatch chile peppers. If you’re using frozen (no need to thaw) or canned peppers (no need to drain), they are likely already roasted, peeled and seeded. In some cases they are already coarsely chopped, too – if not, then coarsely chop them and set aside.
In a large mixing bowl, whisk together flour and about 2 teaspoons each of salt and freshly ground pepper. Toss beef in the flour mixture to coat. Heat 2 tablespoons of oil in a Dutch oven (at least 5 quarts) over medium-high heat until just smoking. Add beef in batches and sear until dark brown on all sides. Be sure not to crowd beef too much. Using tongs, remove cooked beef to a plate. Continue to cook remaining beef in batches, so you're not crowding the beef pieces.
Add onion, garlic and jalapeño peppers to the pot and season with salt and freshly ground pepper. Cook over medium-high heat, scraping the bottom of the pot with a wooden spoon to dislodge browned bits. Add an additional tablespoon of oil if necessary to keep the caramelized bits of onion mixture and beef (know as “fond”) from scorching. You can also add a splash of stock at this point. Cook for about 5 to 7 minutes or until the onion has begun to soften and brown.
Add cumin, coriander and Mexican oregano and cook for an additional 2 minutes.
Stir in tomato paste and beer. Bring to a boil and cook until liquid has reduced by about two-thirds. Scraping the bottom of the pan to loosen any bits of fond.
Stir in stock and return beef to pot. Add reserved poblano and hatch chili peppers. Bring to a boil and reduce heat to a simmer. Cook, covered for 2-1/2 hours or until beef is fork tender.
Remove chili from heat and serve in bowls with chopped cilantro, corn chips or flour tortillas and a wedge of lime. A splash of acid always brightens the flavor.