To braise the pork belly, preheat the oven to 425 degrees F. Remove the skin from the belly and use a sharp knife to score the fat cap. Place the belly in a roasting pan large enough to hold it in a single layer and set aside.
In a mixing bowl, combine 2 cups of water with the pear juice, soy sauce, mirin, sugar and vinegar. Mix well to combine, pour the mixture over the belly and cover the pan tightly with aluminum foil. Place the pan in the oven and braise for 30 minutes. Reduce the temperature and cook an additional 3 to 4 hours, or until the belly is tender. Remove the pan from the oven and allow to rest 5 to 10 minutes before carefully removing the belly from the braising liquid and cutting into 1-ounce pieces. Keep the pieces warm.
Prepare the other components of the recipe while the belly is braising. For the pickles, combine the pears, pear juice, onions and vinegar in a non-reactive container with a tight-fitting lid. Shake gently to combine and store in the refrigerator several hours, at least as long as the belly is in the oven.
For the sauce, combine the peppers, pears and 1/4 cup of the pear juice in the jar of a blender. Puree until smooth, adding more pear juice as needed for consistency and flavor. Refrigerate until ready to use.
To prepare the slaw, combine the cabbage and Brussels sprouts in a bowl. Sprinkle the salt and pepper over top and use your hands to toss the ingredients together. Add the yogurt and stir to evenly coat the cabbage and sprouts. Refrigerate until ready to use.
To serve, saute the pork belly pieces in a hot pan until they are slightly crisp. Place 2 tortillas per serving on a plate and top each one with 1/8 cup slaw, a piece of crispy pork belly, and some pickled onions and pears. Drizzle with sauce and serve immediately.