Melt the butter and olive oil in a large Dutch oven over medium heat. Add the bell pepper, poblano pepper, onion, chili powder, cumin, coriander, sea salt, and freshly cracked pepper to taste. Sweat the mixture for 5-6 minutes or until the veggies begin to soften.
Add the minced garlic, and stir constantly for 1 minute.
Whisk in 3 tablespoons of flour and cook for 2 minutes.
Add the broth and milk, then whisk until smooth.
Add the rice and let it simmer (DO NOT LET IT BOIL) for 25 minutes, or until the rice is tender. Side Note: If you don't plan to eat the entire batch of soup, cook the rice separately and add it to the bowls before eating it.
Combine the cheese with the remaining 3 tablespoons of flour in a zip-lock bag; toss to coat. Side Note: Coating the cheese with flour before adding it to the soup helps prevent the cheese from separating in the soup.
Add the cheese to the soup a handful at a time, stirring to melt completely before adding the next handful.
Stir in chicken and cilantro and cook for 3-5 minutes. Taste the soup and re-season if needed.