Heat a skillet over medium heat with butter or oil.
Season chicken with ½ teaspoon of the salt and pepper, then sear until golden brown, about 4 minutes per side.
Remove the chicken and set it aside. In the same pan, add more butter or oil, then sauté onions, sliced poblanos, and garlic for 5 minutes.
Transfer the sautéed poblano, onion, and garlic mixture to a blender. Add cilantro, ¼ teaspoon salt, and ½ cup chicken stock. Blend until smooth.
Pour into the skillet along with the remaining stock, cream, lime juice, honey, and salt.
Bring to a simmer, return the chicken, cover, and cook until it reaches 165°F.
Adjust consistency with stock if needed. Serve with pasta or mashed potatoes.