Combine pork, water, and 1/2 teaspoon salt in a Dutch oven over medium heat. Cover and cook for 20 minutes, stirring every 5 minutes. Uncover, increase the heat to medium-high, and cook, stirring constantly, until water evaporates, 2 to 3 minutes. Continue to cook until pork has browned in its rendered fat, 15 to 20 more minutes.

Meanwhile, stem dried chile peppers and discard seeds. Place chiles into a large skillet over low heat just until they start to soften; don't toast them. Transfer to a bowl of hot water and soak for 20 minutes.

Transfer pork to a plate, leaving all drippings in the Dutch oven.

Drain chiles and reserve soaking water. Place chiles into a blender with cilantro, bouillon, garlic, bay leaves, peppercorns, cloves, cinnamon stick, oregano, thyme, and cumin seeds. Pour in 1 cup reserved soaking water and blend until combined. Pour in 1 more cup soaking water, season with salt, and blend until completely smooth.

Place the Dutch oven over medium heat and add lard to the drippings. Very carefully add blended chile mixture, being careful as it may splatter. Scrape up any browned bits from the bottom. Bring to a boil, then add pork and any accumulated juices.

Reduce the heat and cover partially, leaving about 1 inch uncovered. Simmer, stirring occasionally, until sauce has thickened and reaches the desired consistency, 15 to 20 minutes.