Prep the chicken: Pat chicken dry.
Season both sides with 1 teaspoon salt, 1/2 teaspoon black pepper, and half the cumin, coriander, oregano, and smoked paprika.
Sear for flavor: Heat a large skillet over medium-high. Add oil. Sear chicken 3–4 minutes per side until golden.
Remove to a plate. It doesn’t need to be fully cooked yet.
Build the base: Lower heat to medium. Add onion and a pinch of salt.
Cook 3–4 minutes until softened. Stir in garlic and jalapeño (if using) for 30 seconds.
Spice it right: Add the remaining spices to the pan. Toast 30 seconds to wake them up.
Add chiles and broth: Stir in green chiles and chicken broth.
Scrape any browned bits from the pan. Simmer 3 minutes.
Thicken gently: Whisk cornstarch with 2 tablespoons water. Stir into the pan and simmer 1–2 minutes until slightly thickened.
Finish the sauce: Turn heat to low.
Stir in Greek yogurt, lime zest, and 1–2 teaspoons lime juice. Taste and adjust salt, pepper, and lime. The sauce should be tangy and savory, not sour.
Smother and cook through: Nestle chicken back into the sauce.
Spoon sauce over the top. Cover and simmer on low 6–10 minutes, until the chicken reaches an internal temperature of 165°F.
Optional cheese melt: Sprinkle a light layer of shredded cheese over the chicken. Cover for 1–2 minutes to melt.
Finish and serve: Scatter cilantro and extra lime juice if you like.
Serve with brown rice, cauliflower rice, quinoa, or warmed tortillas.