Add pork, water, and salt to a Dutch oven. Cover and simmer on medium for 20 minutes, stirring occasionally. Uncover, increase heat to medium-high and cook until water evaporates and pork is golden in its fat (another 15–20 minutes). Remove the pork, leaving the flavorful fond intact.

Toast chiles lightly without burning, then soak in hot water until soft (about 20 minutes). Blend with cilantro, bouillon, peppercorns, garlic, cinnamon stick, oregano, thyme, cumin, bay leaves, and cloves, using soaking water for a smooth sauce. Season to taste.

Heat lard in the Dutch oven. Add the chile sauce, scraping up fond. Return pork to the pot, bring to a simmer, partially cover, and cook for 15–20 minutes until the sauce coats the pork and flavors meld.

Heat oil, toast rice until golden. Stir in tomato sauce, water, chili powder, tomato bouillon, and garlic. Bring to a boil, reduce to low, cover, and simmer for 20 minutes until liquid is absorbed.

Let the rice rest covered for 5–10 minutes, then fluff. Serve the stew alongside or atop rice, and garnish with fresh cilantro or lime wedges. Warm tortillas or cornbread pair beautifully with the meal.