In a large Dutch oven, heat the oil over medium heat. Add the sweet potatoes and cook, stirring occasionally, until lightly golden, 5 to 7 minutes. Add the onion, bell pepper, and poblano to the Dutch oven. Cook over medium heat, stirring occasionally, until softened, about 10 minutes. Stir in the garlic, cocoa powder, chili powder, cumin, salt, oregano, and pepper. Cook, stirring, for 30 seconds.
Stir in the tomatoes, black beans, pinto beans, and vegetable broth. Bring to a boil over medium-high heat. Reduce the heat to medium-low, cover, and cook, stirring occasionally, until the flavors meld and the potatoes are tender, about 20 minutes.
Mix the masa harina with the warm water and stir it into the pot. Simmer for 15 minutes more.
Stir in the cilantro and lime juice. Add more salt and pepper to taste.
To serve, top each bowl of chili with sour cream, cheese, green onion, avocado, and more cilantro. Serve with lime wedges and tortilla chips.