Sprinkle the pork on all sides with the garlic powder and plenty of salt and pepper.
Heat the pork fat over medium-high heat in a small, heavy Dutch oven or braiser (see Cook's Note). Add the pork and fry on all sides until well browned, about 20 minutes. Add the Coca-Cola and 1/2 cup water (there should be just enough liquid to cover the sides of the meat). Bring to a boil and reduce to a simmer. Add the tarragon, bay leaves and thyme. Cover and simmer until the pork is tender, about 1 1/2 hours; the Coca-Cola will caramelize and the liquid will evaporate completely.
Transfer the pork to a cutting board and shred. Serve with warm corn tortillas (charred over a flame) and toppings on the side: salsa verde, diced onions, cilantro, radishes, lime wedges and avocado.
You can get pork fat from your local butcher, which adds extra flavor when frying. If unavailable, substitute a neutral oil such as canola or vegetable oil. We use a 1 1/2-quart braiser to cook the pork and recommend you use something similar; the pork should crowd the pan a little so that it stays moist.