To roast the green chiles and red pepper, preheat the oven to 400 degrees F. Rub the peppers with a bit of olive oil and place them on a baking sheet. Roast until the outside skins begin to blister and char, about 30 minutes. Remove the peppers and place them in a resealable plastic bag for 20 minutes to steam. (To shorten this process, you can grill or roast the peppers over your gas stovetop until charred, then steam in the resealable bag.)
Once the peppers have “steamed” in the bag, remove the blistered skin. Slice off the tops and remove the seeds (unless you want tons of heat), then dice the peppers.
Heat a large skillet over medium-low heat and add the olive oil. Stir in the onion, roasted peppers and garlic. Cook until the onions soften, about 5 to 6 minutes. Increase the heat to medium and add in the turkey and beef with the salt and pepper, using a wooden spoon to break it apart and combine it. Cook until browned. Stir in the tomato paste, paprika and brown sugar. Stir in the tomato puree, Worcestershire and apple cider vinegar. Cover and cook for 15 to 20 minutes, stirring often. Taste and adjust to your preferences – more salt or pepper, more sugar if it’s too tangy, more vinegar if it’s too sweet.
To serve. spoon the mixture between buns that are layered with the slaw and bread and butter pickles.