How to Make It
Preheat oven to 425°F. Toss onion with 1 tablespoon oil and ¼ teaspoon each salt and pepper on a rimmed baking sheet. Roast until onion begins to soften, about 10 minutes.
Meanwhile, heat remaining 1 tablespoon oil in a large skillet over medium-high. Pat chicken dry with paper towels and season with remaining ½ teaspoon each salt and pepper. Add chicken to skillet and cook until golden brown, about 3 minutes. Flip and continue to cook until golden brown, about 3 minutes more. Transfer chicken to baking sheet with onion and roast until chicken is cooked through, 10 to 12 minutes.
Transfer chicken and onion to a platter. Spoon salsa verde over top and top with cilantro and cheese. Serve with tortillas and lime wedges, if desired.