Cover beans with 4 inches of water and soak for at least 12 hours, or overnight.

Place the pot with beans and water on the stove and heat to a boil. Reduce heat to medium-low and simmer until beans are soft enough to mash, about 2 hours.

Mash the beans thoroughly with a potato masher and simmer for 1 hour more.

Use an immersion blender to pulverize the beans until smooth. Simmer until water evaporates and beans are reduced to a thick paste.

Add milk, lard, garlic powder, salt, chile pepper, cumin, and cayenne. Cook for 10 minutes.

Preheat the oven to 400°F (200°C).

Transfer beans to a casserole dish, sprinkle with Oaxaca cheese, and cover with foil.