Step 1

Heat oil in a large pot over medium-high. Add chorizo in large chunks; cook until browned, about 2 minutes. Break up chorizo with a wooden spoon. Cook, stirring occasionally, until browned on all sides, about 3 minutes. Transfer to a bowl using a slotted spoon. Discard all but 1 tablespoon drippings in pot.

Step 2

Add onion and poblano to pot; cook, stirring often, until softened, about 5 minutes. Add tomato paste, chili powder, salt, cumin, and garlic powder; cook, stirring constantly, until fragrant, about 1 minute. Add 1 cup beans and mash with a fork. Add broth, chorizo, and remaining beans; bring to a boil. Reduce heat to medium-low and simmer until slightly thickened, about 5 minutes. Top with avocado, cabbage, and cilantro. Serve with lime wedges.