Ingredient Note: Hominy is white or yellow corn that has been treated with lime to remove the tough hull and germ. Dried, ground hominy is the main ingredient in grits. Canned, cooked hominy can be found in the Mexican section of large supermarkets-near the beans.
Heat oil in a Dutch oven over medium-high heat. Add pork and cook, stirring once, until just browned on one or two sides, 1 to 2 minutes. Transfer to a plate using a slotted spoon.
Reduce heat to medium-low; add onion and 2 tablespoons water. Cook, stirring occasionally, until the onion is soft and golden brown and any moisture has evaporated, 5 to 7 minutes. Stir in garlic, cumin and coriander and cook, stirring constantly, until fragrant, 30 seconds to 1 minute. Whisk in the remaining 2 cups water, broth and cornmeal. Bring to a simmer over high heat, stirring often. Add hominy, chiles, pepper and salt; return to a simmer. Reduce heat to medium-low and cook, stirring often, until the onion is very soft and the mixture is thickened, about 5 minutes. Stir in lime juice to taste.
Return the pork and any accumulated juices to the pot; cook, stirring occasionally, until the pork is just cooked through, 1 to 2 minutes.