Preheat the broiler to high. Broil the poblanos (with the oven door ajar to allow steam to escape) to char them all over. Place the chiles in a bowl, cover and let cool. Peel and seed the chiles, then, using a food processor, puree them.
Meanwhile, season the red onion rings with half of the lime juice, salt, pepper and a little EVOO to coat. In a second bowl, mash together the avocado, sour cream, cilantro, fresno chile and remaining lime juice; season to taste with salt.
In a large bowl, combine the beef, pork, pureed poblano, cumin, coriander, paprika, cinnamon, salt and lots of pepper. Mix in the beer and worcestershire. Form the mixture into eight 3-inch patties (a little thinner in the center and thicker at the edges). Drizzle a little EVOO in a large skillet or nonstick griddle over medium-high heat. Add the burgers and cook, turning once, for about 7 minutes for medium-rare. Top with the cheese and tent loosely with foil during the last minute or so of cooking.
Place the burgers on the roll bottoms. Top with the onions and sauce and set the roll tops in place.