1 lb boneless, skinless chicken breast, cut into 1/2 inch pieces
8 ounces cream cheese, cut into cubes
3 1/2 cups shredded cheddar cheese, divided
Roast poblano peppers until skin is charred and blistered. You can do this over the open flame on a gas stove, or by heating your broiler to high and placing poblanos within a few inches of the broiler (turning to get all sides charred).
Place poblanos in a bowl and cover with plastic wrap. Let cool, then rub skin to remove as much as possible. Cut out seeds and then place in a food processor or blender to finely chop. Set aside.
In a large saucepan over medium heat, melt butter. Add onion and cook, stirring frequently, until translucent, about 5 minutes. Add garlic, cumin, and poblanos and stir until fragrant, about 1 minute.
Stir in chicken broth and season to taste with salt and pepper. Bring to a boil and then reduce heat to a simmer. Add chicken pieces and continue to cook until chicken is cooked through, about 10 minutes.
Add cream cheese and two cups of the cheddar cheese and whisk until smooth.
To serve, divide into 6 bowls and sprinkle each with 1/4 cup shredded cheddar cheese. Sit briefly under the broiler until cheese is melted and browned (this step is optional but OH SO GOOD!).