Place dried hominy in a bowl and pour in boiling hot water to generously cover. Let soak anywhere from 2-3 hours.
Drain, place in a large pot, add 12-14 cups water and 5 large garlic cloves. Bring to a rolling boil, reduce the heat to medium, cover partially so steam can escape, and cook for about 1 hour and 30 minutes, just until the hominy softens and it is barely attempting to open or bloom. It should still be firm and toothy and sweet. Turn off the heat, add 2 teaspoons of salt and stir. Fish out the cooked garlic and discard. (Skip this step if using canned hominy.)
Place dried pinto beans in a large pot, cover with the water, and add the white onion half. Bring to a rolling boil, reduce heat to medium, and cover partially so steam can escape. Cook for about 1 hour until the beans are tender, but still slightly firm and not breaking or falling apart. Add the remaining 2 teaspoons of salt and stir. Fish out the cooked onion and discard. (Skip this step if using canned beans.)
In a large pot set over medium heat, add oil. Once hot add the chopped white parts of the scallions. Cook until wilted and barely starting to brown around the edges, about 3-4 minutes. Using a slotted spoon, add all the cooked pintos, and add about 3 cups of their cooking liquid using a ladle or measuring cup. Alternatively, add the 4 cans of beans. Using a slotted spoon, incorporate all the cooked hominy, and add about 3 cups of their cooking liquid using a ladle or measuring cup. Alternatively, add the 3 cans of hominy, along with 3 cups of broth or water.
Raise heat to medium-high and incorporate the sliced jalapeños. Let it all come to a simmer and cook for another 12-14 minutes, until the broth has thickened and become soupy, and the chiles have cooked. Taste for salt and adjust if needed. Turn off heat.
Serve and let your guests garnish their bowls with abundant chopped cilantro, the scallion greens, queso fresco, and Tomato Salsa with Oregano and Chile de Árbol.