In a large pot, combine the pork shoulder, halved onion, garlic cloves, bay leaves, dried oregano, ground cumin, salt, and water.
Bring to a boil over medium-high heat, then reduce the heat to low and simmer for about 2 hours, or until the pork is tender and easily shreds with a fork.
Remove the pork from the pot and shred it into bite-sized pieces. Set aside.
Strain the broth and discard the solids. Return the broth to the pot.
Remove the stems and seeds from the dried guajillo and ancho chiles.
Heat a skillet over medium heat and toast the chiles for about 1-2 minutes until they become fragrant. Be careful not to burn them.
Place the toasted chiles in a bowl and cover them with hot water. Let them soak for about 20 minutes until they become soft. Drain and set aside.
In a blender, combine the soaked chiles, vegetable oil, dried oregano, ground cumin, salt, and a little water (if needed). Blend until smooth.
Add the chile sauce to the pot with the strained broth.
Add the drained and rinsed hominy to the pot with the broth and chile sauce.
Bring to a simmer over medium heat and cook for about 30 minutes, allowing the flavors to meld together.
Add the shredded pork back to the pot and cook for an additional 10 minutes.
Ladle the pozole into bowls.
Enjoy your meal!