Place the pork chunks, salt, peppercorns, half of the onion, 2 cloves of garlic, and bay leaves in a large pot. Cover with water by about two inches. Bring to a boil, then reduce heat and simmer until the pork is very tender, about 2 to 2.5 hours. Skim off any foam that rises.
Remove the pork from the broth and set aside to cool slightly. Strain and reserve 4 cups of the cooking broth. Discard the solids. Once cool enough to handle, shred the pork using two forks.
While the pork cooks, prepare the chile sauce. Place the dried Guajillo and Ancho chiles in a saucepan. Cover with water and bring to a boil. Remove from heat, cover, and let the chiles soak for 30 minutes until soft.
Drain the soaked chiles, reserving about 1 cup of the soaking water. Place the softened chiles in a blender with 2 cloves of fresh garlic, the remaining half onion, Mexican oregano, cumin, and 1 cup of the reserved pork broth. Blend until completely smooth. Add a little soaking water if needed to create a thick paste.
Strain the chile sauce through a fine-mesh sieve into a clean pot, pressing down on the solids to extract all the liquid. Discard the solids left in the sieve.
Add the remaining 3 cups of reserved pork broth to the strained chile sauce. Bring the sauce to a simmer over medium heat. Taste and adjust salt as needed.
Add the shredded pork and the drained hominy to the simmering chile broth. Simmer gently for 20 to 30 minutes, allowing the flavors to combine. Do not boil rapidly.
Serve the pozole hot in bowls, offering the garnishes on the side for each person to customize their soup.
Notes
For a deeper flavor, toast the dried chiles lightly in a dry skillet before soaking them.
If you prefer a quicker method, you can cook the pork in a pressure cooker for about 45 minutes.
Use only white hominy for authentic Pozole Rojo; yellow hominy changes the texture and color.