Heat the oven: Preheat to 375°F (190°C).
Lightly coat a 9x13-inch baking dish with cooking spray.
Sauté aromatics: Warm olive oil in a skillet over medium heat. Add onion and cook 3–4 minutes until softened. Stir in garlic for 30 seconds, just until fragrant.
Mix the filling: In a large bowl, combine shredded chicken, half of the green chiles, half of the cheese, cilantro, cumin, chili powder, lime zest, and half the salt and pepper.
Add the sautéed onion and garlic. Stir to coat evenly.
Make the sauce: In a blender, combine salsa verde, remaining green chiles, Greek yogurt, lime juice, and remaining salt and pepper. Blend until smooth.
If it’s very thick, add a splash of chicken broth. Taste and adjust seasoning.
Soften the tortillas: Lightly spray both sides of the tortillas with cooking spray. Warm in a dry skillet over medium heat for 20–30 seconds per side until pliable, or wrap in a damp paper towel and microwave for 30–45 seconds.
Assemble: Spread 1/2 cup of the sauce on the bottom of the baking dish.
Fill each tortilla with about 1/4 cup of the chicken mixture. Roll tightly and place seam-side down in the dish.
Sauce and cheese: Pour the remaining sauce evenly over the enchiladas. Sprinkle with the remaining cheese.
Bake: Cover loosely with foil and bake for 15 minutes.
Remove foil and bake another 8–10 minutes, until bubbly and lightly browned around the edges.
Rest and garnish: Let the enchiladas rest 5 minutes. Top with more cilantro, green onions, or sliced radishes. Serve with lime wedges.