Prep the oven and pan: Heat oven to 375°F (190°C).
Lightly oil or spray a 9x13-inch baking dish.
Sauté aromatics: Warm olive oil in a skillet over medium heat. Add onion with a pinch of salt and cook 3–4 minutes until translucent. Stir in garlic and cook 30 seconds until fragrant.
Make the light sauce: Lower heat.
Add chicken broth and salsa verde; simmer 2 minutes. Turn off heat and whisk in Greek yogurt, lime zest, and half the lime juice. Season with 1/2 teaspoon cumin, 1/2 teaspoon chili powder, 1/4 teaspoon smoked paprika, a pinch of oregano, salt, and pepper.
Taste and adjust acid with more lime if needed.
Season the chicken: In a bowl, toss shredded chicken with 1/3 cup of the sauce, 2 tablespoons cilantro, a pinch of cumin, salt, and pepper. If using cheese, mix in 1/4 cup.
Soften the tortillas: Wrap tortillas in a damp paper towel and microwave 30–45 seconds until pliable. Alternatively, toast each in a dry skillet 10–15 seconds per side.
Assemble: Spread a thin layer of sauce across the bottom of the baking dish.
Fill each tortilla with a small mound of chicken, roll snugly, and place seam-side down. Repeat with remaining tortillas.
Sauce and cheese: Pour remaining sauce over the enchiladas, covering evenly but not drenching. Sprinkle remaining cheese on top if using.
Bake: Bake 15–18 minutes until warmed through and cheese melts.
If you like some color, broil 1–2 minutes at the end, watching closely.
Finish with lime and herbs: Let rest 5 minutes. Sprinkle with remaining cilantro and a squeeze of lime. Add toppings if you like.
Serve: Pair with a crisp salad, quick slaw, or roasted veggies to keep things light and fresh.