Heat the broiler and place poblano on a foil-lined sheet 6 inches below the heat. Broil for 8 to 12 minutes, turning until blistered on all sides; cover in a bowl for 10 minutes, then peel, seed and finely chop.
Meanwhile, heat oil in a soup pot over medium heat. Cook onion for 7 minutes and garlic for 30 seconds.
Add chicken thighs, broth, salt and cumin. Bring to a gentle simmer, cover partly and cook for 20 to 25 minutes until the thickest thigh reaches 165°F.
Lift chicken onto a plate and shred into short pieces. Add corn and chopped poblano to the broth and simmer for 5 minutes.
Whisk masa harina into the cold milk until smooth. Stir into the simmering broth and cook gently for 5 to 7 minutes, stirring frequently until lightly thickened.
Return chicken and add cream. Warm gently for 2 to 3 minutes, then divide among 6 bowls.