Soak the pinto beans. Pick through the pinto beans and remove any rocks if you see them. Rinse beans well then cover with water and let soak overnight. If you don't have time to do this, you can cook beans from dry, but it will take longer. 

Prep hominy. Drain and rinse hominy. Fill a large saucepan with salted water and bring to a boil over high heat. Add hominy, remove from heat and let blanch while you prep the other ingredients. 

Char the vegetables. Heat broiler to high. Arrange onion, tomatillos, garlic, and jalapeños on a baking sheet. Broil until charred on all sides, turning occasionally. Keep a close eye on the garlic, it will toast faster than the others. Remove it as it gets golden brown, but not burnt. 

Fry the pepitas. Meanwhile, heat 1 tablespoon of the oil in a frying pan over medium heat. Add pumpkin seeds and fry in the oil until toasted and starting to pop. Season with salt and transfer to a blender.

Blend the green sauce. Once vegetables are charred, add them to the blender as well along with 1/2 cup of the water or vegetable broth (if using) and the cilantro. Blend on high until very smooth. 

Fry the sauce. Heat remaining 3 tablespoons of oil in a large soup pot over medium-high heat. Add pureed vegetable mixture (careful, it will spatter), and stir constantly, frying the sauce until thickened slightly, about 5 minutes. Add remaining 5 1/2 cups of water or broth. Drain the soaked pinto beans and add those too. 

Simmer soup until beans are tender. Bring to a boil, then reduce heat to a simmer, cover, and cook until beans are tender, about 1 hour (this will take longer if you didn't pre-soak the beans). 

Add hominy. Drain hominy and add to the pot. Season with salt (start with 2 teaspoons and go from there). Serve with as many garnishes as you can stand.