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Green chile chicken skillet is wonderfully flavorful with zesty Tex-Mex vibes. The tangy sauce is perfect for spooning over cilantro-lime rice.
Stir together cumin, chili powder, coriander and 1/2 teaspoon of the salt in a large bowl. Add chicken and toss until evenly coated, pressing to adhere.
Heat 1 tablespoon of the oil in a 12-inch, oven-safe skillet over medium until shimmering, about 1 minute. Add chicken, rounded side down, and cook, undisturbed, until browned on underside, 6 to 7 minutes. Flip and continue to cook, undisturbed, until other side is browned, 6 to 7 minutes. Transfer chicken to a plate.
Add remaining 2 tablespoons oil to skillet. Stir in onion and poblanos, and cook over medium-high, stirring often, until peppers are softened, 8 to 10 minutes. Stir in broth, and bring to a boil over high.
Nestle chicken between onions and peppers, and reduce heat to medium. Cover and cook until liquid reduces slightly and a thermometer inserted into thickest part of chicken registers 155°F, 6 to 8 minutes. Remove lid and stir in salsa, green chiles, and remaining 1/2 teaspoon salt; bring to a simmer over medium, about 2 minutes. Remove from heat.
Preheat oven to broil. Transfer chicken to a separate clean plate. Stir cream cheese and cilantro into onion mixture until smooth and creamy. Nestle chicken back into skillet. Sprinkle Monterey Jack cheese around chicken. Broil in preheated oven until cheese is melted and lightly browned, about 2 minutes.
Garnish with cilantro leaves. Serve with sliced avocado, Cilantro Rice, and lime wedges.