Season pork on all sides with salt and pepper. Heat oil in a large stock pot over medium-high heat. Add pork and cook until golden brown, about 7-8 minutes. Transfer to a plate and set aside.
Reduce heat to medium and add onions and jalapeños to the pot. Season generously with salt and pepper. Cook until vegetables are tender and lightly browned, about 10 minutes. Add garlic and cook 1 minute more.
Add mole paste and mash with the back of a wooden spoon until it has softened and blended in with the vegetables. Return the pork and any juices to the pot and add the chicken broth. Bring to a boil, then reduce to a simmer. Cover and cook until pork is tender, about 15-20 minutes. Add hominy and cook 5 minutes more.Taste and add more salt and pepper if necessary.
A plethora of garnishes can be served with this soup. I've listed my favorites above, but you can also top with crispy, fried tortilla strips, thinly sliced cabbage or thinly sliced radishes.