Preheat the broiler to high. Arrange the bell pepper and poblano peppers whole on a baking sheet. Broil for about 5 minutes on each side, turning occasionally, until charred and blackened on the outside.
Remove the peppers to a bowl and cover with plastic wrap. When cool enough to handle, remove the skins and seeds/stems/ribs from the peppers. Chop the peppers and use for the chili.
When the peppers are roasted, make the chili. Preheat a soup pot to medium-high heat with the olive oil. When hot, add the chicken and cook, breaking up with a spoon as you go, for about 7 minutes. Add the onion, garlic, and cumin with a sprinkle of salt. Stir to combine, and let the onion cook for about 3 minutes until soft.
Add the remaining ingredients to the pot: white beans and green chiles (not drained), roasted peppers, and stock. Stir to combine and taste; add several more pinches of salt to your preferences.
This chili is mild; feel free to add more cumin or some hot sauce if you'd like.
Let the chili simmer for 10-15 minutes, then serve with any toppings you like. Enjoy!