At least 2 hours, and as much as 4 hours before cooking, evenly sprinkle the 3 teaspoons of kosher salt over the pork, place in a bowl, cover, and put in the refrigerator. Remove from refrigerator about 30 minutes before cooking.
In a large dutch oven, preheat the lard over medium-low heat for at least 10 minutes.
Add the pork chunks, leaving as much space as possible between each piece. Your heat should be just high enough that the oil is gently bubbling around the meat. It should not be at a fast fry.
Cook undisturbed for 30 minutes. Flip, then cook the opposite side for an additional 30 minutes.
Add the balance of your ingredients, reduce the heat to a slow simmer, cover, and cook for an additional 1 1/2 hours.
Remove the pork pieces to a paper-towel-lined plate and let cool for about 5 minutes. Break apart the pork chunks with a fork as you serve them.