Roast the Peppers: Preheat your oven to 400°F (200°C). Line a baking sheet with aluminum foil. Arrange the Anaheim or poblano peppers on the sheet with space between them. Roast in the preheated oven for 8-10 minutes, then use tongs to flip them. Roast for another 8-10 minutes until the skins are blistered.
Steam the Peppers: Remove the peppers from the oven and place them on a cutting board. Invert a large bowl over the peppers to steam them for 30 minutes. Once steamed, cut off the stems, peel the skins, and discard them. Dice the roasted peppers and set aside.
Cook the Aromatics: In a Dutch oven or large heavy pot, heat the olive oil over medium heat. Add the chopped onion and cook until soft and translucent. Lower the heat, then add the minced garlic, cumin, chili powder, marjoram, and cayenne pepper. Stir constantly for 1 minute until fragrant.
Build the Chili: Pour in the chicken broth, and add the beans, corn, cooked chicken, and diced roasted peppers. Stir to combine. Let the chili simmer for 10 minutes.
Puree the Chili: Carefully remove 2-3 cups of the chili from the pot and puree it using an immersion blender or stand blender. Return the pureed chili back to the pot, stirring to combine. Let it heat for an additional 2-3 minutes.
Finish the Chili: Turn off the heat and stir in the sour cream and chopped cilantro, reserving some cilantro for garnish. Season the chili with kosher salt and fresh ground black pepper to taste.
Serve: Ladle the chili into bowls and top with shredded Monterey Jack or Pepper Jack cheese (optional) and a sprinkle of reserved cilantro. Serve hot and enjoy!