In a large soup pot put 3 quarts of water, the pork shoulder, chicken, quartered onion, smashed garlic, and cilantro stems and bring to a boil. Skim any foam that rises to the surface, partially cover the pot, reduce heat to a simmer and cook for 2 1/2 to 3 hours, or until the pork is very tender and the stock is flavorful.

While the meat is cooking, heat a small skillet over medium low heat. Add the pumpkin seeds and cook, stirring constantly, until all of the seeds have popped and turned golden, 3 to 4 minutes. Transfer to a bowl and set aside to cool.

Place the tomatillos in a small saucepan and add enough water to cover by 1-inch. Add 1 teaspoon of the salt and cook over medium heat until the tomatillos are tender, about 10 minutes. Strain tomatillos and discard the cooking liquid. Place the tomatillos in the jar of a blender along with the pumpkin seeds, green chile, and chopped onion.. Add 1/3 cup of the pork cooking liquid and blend until very smooth. Strain through a medium-mesh sieve and discard the solids.

In a skillet over medium high heat, add the oil. When hot, add the puree and cook, stirring constantly, for about 7 minutes, or until the color has darkened and the mixture has thickened considerably. Remove from the heat.

When the pork is very tender, strain the stock. Set the meat and chicken aside. Discard other solids. Return the stock to the soup pot, add the tomatillo-pumpkin seed mixture and the hominy and return to a gentle simmer. Cook for about 1 hour, stirring frequently, until slightly thickened and flavorful. When the meat and chicken are cool enough to handle, discard any bones and shred into bite size pieces. Add the meat to the soup pot and season with the remaining 1 1/2 teaspoons salt. Serve the pozole in shallow bowls, and allow guests to garnish their soup with condiments of their own choosing.