Remove stems from poblano peppers. Place peppers on a gas cooktop. Cook on high heat on all sides until outer flesh is fully blackened, about 5-10 minutes.
Place charred peppers in a medium mixing bowl and cover with plastic wrap. Let sit for 10 minutes or until peppers are cool enough to touch.
Remove blackened skins from peppers; chop peppers into a small dice and set aside.
In a dutch oven or a stockpot, heat olive oil over medium high heat. Add chicken to oil and cook 3-4 minutes per side, or until chicken is browned. Work in batches if necessary to keep from overcrowding the pan. Remove chicken and set aside.
Melt butter over medium heat. Add onions and peppers. Cook until onions are cooked through, about 3-5 minutes. Add in garlic and flour and cook, stirring contstantly, until all raw flour is gone.
Add in cumin, salt and pepper. Mix until well combined.
Add in broth and bouillon. Stir well, scraping up browned bits from the bottom of the pot. Cover and reduce heat to medium low.
Cube up chicken while soup comes to a simmer.
Add in chicken and juices on the chicken plate and stir. Add in cream cheese in small spoonfuls (this helps the cream cheese melt faster). Stir and cover again. Simmer for 10 minutes, or until cream cheese is melted. Add in cheddar, stir to melt.