In a 6 quart slow cooker, combine the chicken, garlic, onion, salt, cumin seeds, hominy, broth, and water. Cover and cook on low for 4 hours, until chicken is tender and cooked through. Remove the chicken and let cool. Discard the bones and skin and break the meat into large pieces. Refrigerate until needed. Add the cilantro and continue cooking the soup on low for another 2 hours.
While the soup is cooking, make the salsa. Heat a 10 inch skillet over medium. Toast the pepitas in the dry pan, until crunchy and olive green. Let cool.
Place the tomatillos in a small pot and cover with cold water. Bring to a simmer over medium high heat and simmer for 5 minutes. Drain and place in a blender with the pepitas, onion, garlic, chiles, and cilantro. Add 1/2 cup broth from the slow cooker and puree, scraping the sides of the blender as needed, until very smooth.
Heat the saute pan over medium and add the vegetable oil. Pour in the contents of the blender. Cook, stirring often, until the sauce is thickened and pale green, 5 to 7 minutes. If the sauce splatters, reduce the heat.
To finish the soup, discard the onion, garlic, and cilantro sprigs. Stir in the salsa and chicken. Cook on low for 30 minutes. Serve with garnishes.