Instructions

Adjust oven rack 6 inches from broiler element and heat broiler. Arrange poblanos skin side up on aluminum foil–lined rimmed baking sheet. Broil until skins are well charred, 6 to 8 minutes, rotating sheet halfway through broiling. Transfer poblanos to bowl, cover with plastic wrap, and let steam for 5 minutes. Using spoon, scrape charred skin from poblanos (do not rinse to remove skin). Slice peppers into ¼-inch-thick strips; set aside.
Pat chicken dry with paper towels and sprinkle all over with pepper and ½ teaspoon salt. Heat 1 tablespoon oil in 12-inch nonstick skillet over medium-high heat until shimmering. Add chicken and cook until browned on both sides, 3 to 5 minutes per side. Transfer chicken to plate.
Reduce heat to medium. Add remaining 1 tablespoon oil, onions, and ¼ teaspoon salt to now-empty skillet and cook, stirring occasionally, until onions are lightly browned and beginning to soften, about 5 minutes. Add garlic, poblanos, and remaining ¼ teaspoon salt and cook until fragrant, about 1 minute. Add crema and bring to boil. Nestle chicken into poblano mixture. Reduce heat to medium-low, cover, and cook until chicken registers 160 degrees, 10 to 12 minutes.
Transfer chicken to carving board, tent with aluminum foil, and let rest for 5 minutes. Return skillet to medium heat and cook until spatula leaves distinct trail when dragged through pepper mixture, 2 to 4 minutes. Off heat, stir in cilantro and lime juice. Season with salt and pepper to taste. Slice chicken and serve with rajas.