Heat the oil in a large pot over medium heat. Add the fennel, chorizo, and ½ teaspoon each salt and pepper. Cook, stirring occasionally, until the fennel is tender, 8 to 10 minutes.
Add the broth and bring to a boil.
Add the fish and hominy. Reduce heat and simmer until the fish is opaque throughout, 2 to 4 minutes.
Serve topped with the cilantro and lime wedges.