For the Soup: Heat pumpkin seeds in the base of a large Dutch oven over medium-high heat, stirring constantly, until they start to pop and smell nutty, about 4 minutes. Transfer pumpkin seeds to a bowl and set aside.

Add chicken, tomatillos, onion, peppers, chicken stock, oregano, epazote (if using), and a large pinch of salt to the Dutch oven. Bring to a boil over high heat, then reduce to a bare simmer. Cook, stirring occasionally, until chicken and vegetables are completely tender, about 40 minutes.

Using tongs, transfer chicken to a large plate or bowl and set aside. Discard epazote sprigs (if using). Set a large fine-mesh strainer over a large bowl and strain the broth through it. Transfer solids to the jar of a blender. Add pumpkin seeds and cilantro to the blender. Blend on high speed until smooth. Set aside.

Using a ladle, carefully skim off a few tablespoons of fat from the strained stock and add it to the Dutch oven (it's okay if a little stock gets in as well). Heat over high heat, swirling and stirring until the watery stock completely evaporates and starts to form a browned layer in the bottom of the pan. (It will spatter a bit. The more you stir, the less it will spatter.) As soon as the chicken fat starts to smoke, pour in the contents of the blender all at once and cook, stirring, for about 15 seconds (it will spatter a lot—wear an apron!). Immediately pour in strained chicken stock and fat and stir to combine. Bring to a bare simmer, stir in hominy, season to taste with salt, and keep warm.

By this stage, the chicken should be cool enough to handle. Discard the skin and bones and shred the meat into bite-size pieces with your fingertips. Stir the picked chicken back into the soup.

To Serve: Ladle the hot soup into bowls and garnish with diced avocado and radish, sliced chiles, chopped cilantro, and chopped white onion. Serve immediately.