Using tongs, roast the poblano peppers over a gas flame until charred all over. Alternately, place the peppers on a baking sheet and broil under high heat until blistered. Transfer the peppers to a ziplock bag or heat-safe mixing bowl and cover with plastic wrap.
Once the peppers are cool, peel and dice them.
In a heavy bottomed pot, heat the olive oil over medium-high heat. Add the diced onion, peppers, and jalapeños and sauté for 2-3 minutes until the onion is softened.
Add the cream cheese and spices to the pot and stir really well, until the cream cheese is smooth. Then, add the beans. Use a fork or potato masher to mash them slightly. Add the chicken and corn and stir well so that everything is well-coated by cream cheese.
Add the broth, stir, and bring to a simmer. Lower the heat and simmer on medium-low for 30 minutes, stirring occasionally. Once the chili is thick, season to taste with salt and pepper.