The beans. Rinse the beans, then scoop them into a large (6-quart) pot (preferably a Dutch oven or a Mexican earthenware olla), and add 2 quarts of water and remove any beans that float. Bring to a boil, reduce heat to medium-low, and simmer, partially covered, until the beans are thoroughly tender (they will taste creamy, not chalky), about 2 hours. You’ll need to stir the beans regularly and add water as necessary to keep the level of the liquid a generous 1/2 inch above the level of the beans.
The chiles. While the beans are cooking, make the chile purée. On an ungreased griddle or heavy skillet over medium heat, toast the dried chipotles, turning regularly and pressing flat with a spatula, until they are very aromatic and a little toasty smelling, about 30 seconds. (Canned chipotles need no preparation.)
On the same hot surface, toast the anchos: open the chiles out flat and, one or two at a time, press flat for a few seconds with a metal spatula until they start to crackle, even send up a faint wisp of smoke, then flip and press down to toast the other side. In a small bowl, cover both kinds of toasted chiles with hot water and let rehydrate 30 minutes, stirring frequently to ensure even soaking. Drain and discard the water.
In a food processor or blender, purée the chiles with garlic, onion, and about 1/2 cup water (you may need a little more water to get everything freely moving through the blades). Press through a medium-mesh strainer into a bowl. In a large saucepan, heat 2 tablespoons of the oil or lard over medium-high. Add the purée all at once and stir nearly constantly as it sears and thickens for about 5 minutes. When the beans are tender, scrape the chile purée into them, stir well, and simmer 30 minutes longer.
The masa dumplings. In a large bowl, knead together (your hand works best here) the fresh or reconstituted masa with the remaining 2 tablespoons of oil or lard, 1/2 teaspoon of the salt, 1/4 cup of the chopped cilantro, and the cheese until uniformly mixed. Form into about 48 balls, each the size of a large marble. Cover and set aside.
Finishing the dish. Check the consistency of the black bean stew; there should be a good amount of broth in the beans (you have to add the dumplings and greens and still come out with a stew-like consistency, so add additional water if necessary) and the broth should be as thick as a light sauce. (If it’s not as thick as you’d like, purée a cup of the beans in a food processor or blender and return to the pot as thickening.) Liberally season the stew with salt, usually about 2 teaspoons (the beans themselves will continue to absortb the salt for quite a while after you season them).
With the pot simmering over medium, add the dumplings one at a time, nestling them into the gurgling broth as they go in. Simmer 5 minutes, then add the greens; stir gently so as not to break up the dumplings, and simmer until the greens are fully cooked (about 7 minutes for tender greens like chard, 10 to 12 minutes for tougher ones like collard and lamb’s quarters).
Ladle into warm bowls, sprinkle liberally with the remaining chopped cilantro, and serve with plenty of steaming tortillas for a really satisfying meal.