Heat a large Dutch oven over medium-high heat. Add the olive oil, then onion and poblano pepper. Season with ½ teaspoon of salt and cook until slightly softened, stirring occasionally, about 5 minutes. Add the garlic and jalapeño, and cook for 2 minutes more. Add the cumin, coriander, chili powder, black pepper, and oregano, and cook until fragrant, 1 minute more.
In a small measuring cup, whisk together ½ cup of chicken broth and the cornmeal or masa harina.
Add the remaining 3 ½ cups chicken broth, cornmeal mixture, white beans, canned green chilis, and corn to the Dutch oven. Bring to a simmer and cook, stirring occasionally, for 10 minutes, over medium heat. Stir in the chicken and cook for 5 minutes more. Stir in the heavy cream, lime juice, and cilantro, and remove from the heat. Season with the remaining ½ teaspoon of salt, plus more to taste.
Serve topped with additional cilantro, tortilla chips, shredded cheese, and sour cream.
