In a large pot or Dutch oven, combine sliced onion, garlic, bay leaves, and Mexican oregano with the pork shoulder. Fill with enough water to cover and bring to a boil. Then simmer for 3 to 4 hours until tender.

Carefully remove the pork, allow it to cool, shred it using forks, and set aside, reserving the broth.

In a separate pot, bring water to boil, add hominy, and cook for 5-10 minutes. Drain and set aside.

Rinse ancho and guajillo chiles, removing stems and seeds, then toast in a skillet for 2-3 minutes until fragrant.

Soak toasted chiles in hot water for 30 minutes until softened.

In a blender, combine soaked chiles, onion, garlic, and some soaking water. Blend into a smooth sauce.

In the pot, heat oil, add the blended sauce, and cook for 5-7 minutes until thickened.

Add shredded pork and drained hominy to the pot with reserved broth. Simmer for 30 minutes.

Serve in bowls, garnished with diced onion, oregano, radishes, and cilantro.