If using pre-made Mole paste, skip the "Prepare Chiles" and "Prepare Vegetables" steps below.Prepare Chiles - Boil some water. Tear peppers into flat pieces and toast them in a large heavy skillet over medium heat. Press them down for a few seconds then flip. Do the same thing on the other side. When they begin to smell and change color, remove and toss in a bowl. When all done, pour boiling water over them and cover with a small plate to keep submerged. Soak for 30 minutes while preparing the vegetables. Prepare Vegetables - Peel 2 of the garlic cloves, peel, slice and put aside. Roast the remaining unpeeled garlic cloves in the same skillet with unpeeled onion halves cut-side down over medium-low heat. Turn frequently. Remove garlic cloves after 8-10 minutes to cool slightly. Let onions cook for another 10-12 minutes and remove to cool. When cool enough to handle, lightly scrape char off exposed part of onion and peel both garlic and onion over a bowl. Place peeled garlic, onion and any juices into the bowl of a food processor or blender. Add tomatoes and tomatillos with juices to same bowl. Drain chilies and add. Add in 1 cup water and bread pieces. Process on high until a smooth paste forms. Scraping down the sides occasionally. Strain into a bowl using a wooden spoon to extract as much paste as possible.
Cooking the Meats - Salt and pepper meat and chicken pieces. Heat ⅓ cup oil over medium-high heat in a large lidded Dutch oven or casserole. Starting with the pork cubes, brown uncrowded about 2 minutes per side. Remove browned pieces to a separate bowl. When done with pork pieces, add chicken in single, uncrowded layers and brown 3 minutes per side. Remove and set aside with pork.
Making the Sauce - Add 2 tbsp oil to same pot over medium heat. Add sliced garlic and lightly brown but don't burn, around 1-2 minutes. Remove and discard. Add bay leaf, cinnamon, cumin, ground black pepper, oregano and thyme and cook for 1 minute. Turn up heat to medium high and pour in chile-tomato mixture and 2 cups water. Scrape bits from bottom and cook, covered, for about 20 minutes to blend flavors.
Finishing the Dish - Stir in pineapple chunks and pork cubes and simmer, covered, 15 minute over low heat. Return chicken to pot along with apple wedges and simmer, covered, until the chicken is cooked through, about 20 minutes more. Remove bay leaves and stir in sugar and vinegar. Season with salt and pepper. Remove from heat and serve on dinner plates with corn tortillas on the side.