Broil the poblanos 4 inches from the heat for 8 minutes, turning twice, until blistered and blackened on all sides.
Cover the peppers for 10 minutes, then peel, seed and dice them without rinsing.
Heat the oil in a Dutch oven over medium-high heat and cook the chicken with 1 teaspoon salt for 6 to 8 minutes until it reaches 165°F; transfer it to a plate.
Cook the onion for 5 minutes, stir in the cumin, then add the poblanos, beans, broth and remaining salt and simmer for 18 minutes.
Return the chicken, lower the heat, stir in the cream and lime juice, and warm for 3 minutes without boiling.