Broil the poblanos 4 inches from the heat for 8 to 10 minutes, turning, until blistered; cover for 10 minutes, then peel, seed and dice.
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, add the garlic and cumin for 30 seconds, then stir in the poblanos, beans, broth and remaining salt.
Mash about 1 cup of beans against the side of the pot and simmer for 15 minutes.
Return the chicken, lower the heat, stir in the cream and lime juice and warm for 3 minutes without boiling.