Cover the pork in a large pot with water and add 2 cloves garlic, salt, and enough water to cover. Bring to a boil then turn the heat down to low and cook uncovered until tender, about 1 1/2 hours. When meat is ready, remove from the heat and shred with two forks.
Meanwhile, as the pork is cooking, place the tomatoes and remaining garlic on a foil-lined baking sheet, and place under the broiler for 15 minutes, turning occasionally. Add the garlic and continue to cook for 3-5 more minutes. Skins should be charred. Place in a blender and puree until smooth.
Heat the oil in a pan and cook the onions until translucent, about 5 minutes. Add tomato puree and chiles and cook at medium heat for about 5 minutes. Add the salt then taste and adjust seasonings.
Stir in the shredded pork, and cook for 10 minutes. Taste and adjust seasonings, adding more salt if needed and pepper to taste.