Place pork shoulder, quartered onion, smashed garlic, bay leaves, salt, and peppercorns in a large pot. Cover with water by about 2 inches. Bring to a boil, then reduce heat and simmer for 1.5 to 2 hours, or until pork is tender. Skim off any foam or impurities during cooking.
While the pork simmers, prepare the chile sauce. Soak the guajillo and ancho chiles in hot water for 20 minutes until softened.
Drain the chiles and place them in a blender with 2 cups of the pork cooking liquid, dried oregano, and cumin. Blend until smooth. Strain the sauce through a fine-mesh sieve into a bowl, discarding any solids.
Once the pork is tender, remove it from the pot and shred or cube it. Discard the onion, garlic, and bay leaves from the cooking liquid.
Return the pork to the pot. Add the drained hominy and the strained chile sauce. Stir to combine.
Bring the pozole to a simmer and cook for at least 30 minutes to allow the flavors to meld. Season with salt to taste.
Serve hot, with your favorite garnishes.
Notes
For make-ahead convenience, prepare the pozole up to the point of adding the hominy and chile sauce. Cool completely, then refrigerate. Reheat gently and add hominy and chile sauce before serving.
This recipe makes a large batch, ideal for family gatherings or freezing for later.
Consider using a sous-vide precision cooker for perfectly tender pork before shredding.