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