Break the stems off the chiles de arbol and ancho chiles and shake out as many seeds as possible. Put the chiles in a bowl and cover with boiling water; weigh down the chiles with a plate to keep them submerged and soak until soft, about 30 minutes. Transfer the chiles and 1 1/2 cups of the soaking liquid to a blender. Add the smashed garlic and 1/2 teaspoon salt and blend until smooth. Strain through a fine-mesh sieve into a bowl, pushing the sauce through with a rubber spatula; discard the solids.
Rub the pork all over with the cumin and 1/2 teaspoon salt; set aside. Heat the vegetable oil in a Dutch oven or pot over medium heat. Add the onion and cook, stirring occasionally, until soft, about 5 minutes. Add the chopped garlic and cook 2 minutes. Increase the heat to medium high. Push the onion and garlic to one side of the pot; add the pork to the other side and sear, turning, until lightly browned on all sides, about 5 minutes.
Stir in 2 cups water, the chicken broth, oregano, bay leaf, 1/2 teaspoon salt and 1/2 cup to 3/4 cup of the chile sauce (depending on your taste). Bring to a low boil, then reduce the heat to maintain a simmer. Partially cover and cook, turning the pork a few times, until tender, about 3 hours.
Stir in the hominy and continue to simmer, uncovered, until the pork starts falling apart, about 1 more hour. Remove the bay leaf. Transfer the pork to a cutting board; roughly chop and return to the pot. Add some water or broth if the posole is too thick. Season with salt. Serve with assorted toppings and the remaining chile sauce.