How to Make It
In a pot, combine the water, garlic head, shallot, thyme, bay leaf, peppercorns, 1 tablespoon of salt and 2 teaspoons of sugar and stir until the salt and sugar are dissolved. Add the pork and refrigerate overnight.
Preheat the broiler. On a rimmed baking sheet, toss the tomatillos with the canola oil. Broil for 20 minutes, stirring, until the tomatillos are softened and nicely charred. Scrape the charred tomatillos into a blender. Add the pineapple, crushed garlic cloves, onion, serrano and habanero chiles, cilantro and the remaining 1 teaspoon of sugar; puree until smooth. Season the tomatillo salsa with salt.
Reduce the oven to 350°. Bring the pot with the pork to a boil over moderate heat. Cover and braise in the oven for 2 hours and 30 minutes, until the pork is very tender.
Transfer the pork to a work surface and cool slightly; discard the liquid. Thinly slice the pork and serve with the salsa, tortillas, chopped white onion, cilantro and guacamole.