Place pork chunks in a large heavy-bottomed pot or Dutch oven. Add orange half, quartered yellow onion, 4 cloves garlic, bay leaves, 2 teaspoons salt, lard or vegetable oil, and 4 cups water. Bring to a boil over high heat.

Once boiling, reduce heat to low, cover, and simmer for 2 to 2.5 hours, or until the pork is extremely tender and easily shredded with a fork.

Remove the pork from the pot and shred it using two forks. Discard the orange, onion, garlic cloves, and bay leaves. Reserve the cooking liquid.

Return the shredded pork to the pot. Add a little of the reserved cooking liquid (if needed) and increase heat to medium-high. Cook, stirring occasionally, until the pork is browned and slightly crispy. Set the crisped carnitas aside.

In the same pot (or a separate large pot), add 1 tablespoon of oil if necessary. Sauté the diced white onion until softened, about 5 minutes.

Add the minced garlic, dried Mexican oregano, and ground cumin. Cook for 1 minute more until fragrant.

Pour in the chicken broth and crushed tomatoes. Add the chipotle peppers in adobo. Bring to a gentle simmer, then reduce heat and cook for at least 20 minutes to allow the flavors to meld.

Stir in the drained hominy and the crisped carnitas. Continue to simmer for another 10-15 minutes, or until everything is heated through. Stir in the chopped fresh cilantro.

Ladle the Carnitas Caldo into bowls. Serve hot with your desired toppings: chopped white onion, fresh cilantro, lime wedges, sliced radishes, avocado, and a dollop of Mexican crema or sour cream.