Preheat a grill to medium and place a cast-iron skillet on top. Add the chiles and cook until softened and the skin is charred, about 10 minutes. Transfer the chiles to a bowl, cover and let cool slightly. Remove and discard the stems, skin and seeds; finely chop the chiles.
Meanwhile, cook the bacon in the skillet until crisp. Discard all but 1 tablespoon of bacon fat; chop the bacon.
In a large bowl, combine the chopped bacon, the reserved bacon fat, the beef and half of the chiles. Form into 6 patties; season with salt and pepper.
In a medium bowl, combine the queso fresco, mayonnaise, buttermilk, 1 tablespoon olive oil and the remaining chiles. Season with salt and pepper, cover and refrigerate.
In another bowl, toss the avocados, cilantro, onion and remaining 1 tablespoon olive oil; set aside.
Grill the burgers, flipping once, for about 10 minutes for medium-rare. Just before the burgers are finished cooking, grill the buns until toasted, about 1 minute. Place a burger on each bun bottom, top with some of the avocado salad, drizzle with some of the queso fresco dressing and set a bun top in place.