1. To make the red chile paste, heat 2 cups (500ml) of water in a saucepan. Remove from heat, cover, and set aside. Cut the dried chiles in half. Heat a heavy-duty skillet over medium heat. Toast the chiles in the skillet, turning them frequently, until fragrant, which will take just a minute or two, depending on how hot the skillet is. (Don’t let them burn.) Place the chiles in the saucepan of warm water, cover, and let stand 15 minutes.
2. Put the chiles in a blender, reserving the liquid, and puree the chiles with the onion and garlic, adding just enough of the reserved liquid to allow the blades of the blender to puree the mixture, scraping down the sides as needed. (I added about 1/2 cup/125ml of the liquid.) Pass the chile puree through a mesh strainer using a flexible spatula, into a bowl, discarding the skins and any errant seeds. Set aside. (The red chile paste can be made in advance, and either refrigerated for several days or frozen.)
3. To make the soup, put the chicken and pig’s foot or chicken feet and back (if using) into a large pot along with the chopped onion, garlic, bay leaves, black peppercorns, and salt. Add 8 to 10 cups water, just enough to just cover the chicken. Bring to a boil, then reduce heat to a steady simmer, partially cover, and let cook for 1 hour.
4. When the chicken has finished cooking, remove the legs and thighs to a plate. Strain the stock through a mesh sieve into a large bowl and chill thoroughly, preferably overnight. When the chicken is cool enough to handle, remove the skin from the chicken and shred the meat into a bowl. Refrigerator the chicken until ready to use.
5. To finish the soup, skim the fat off the surface of the stock. Put the red chile paste in Dutch oven or large soup or stockpot*. Gradually whisk in 6 cups (1,4l) of the stock, then add the chicken meat and hominy. (You can start with the smaller amount of hominy, and add more if you want the soup thicker.) Bring the soup to a near boil. Once hot, taste and add additional salt, if desired. If the soup is too thick, you can add reserved hominy cooking liquid or additional stock.