Prep the oven and pan. Preheat your oven to 375°F (190°C).
Lightly grease a 9x13-inch baking dish with cooking spray or a teaspoon of oil.
Soften the tortillas. If using corn tortillas, wrap them in a damp paper towel and microwave for 30–45 seconds to prevent cracking. Set aside.
Sauté aromatics. Warm olive oil in a skillet over medium heat. Add onion and cook until softened, about 4–5 minutes.
Stir in garlic for 30 seconds until fragrant.
Season and add chiles. Sprinkle in cumin, chili powder, salt, and pepper. Stir in diced green chiles and cook 1 minute to bloom the spices.
Make the light white sauce. In a bowl, whisk cornstarch into the chicken broth until smooth. Pour into the skillet and bring to a gentle simmer, stirring until slightly thickened, 2–3 minutes.
Remove from heat and whisk in Greek yogurt. If it feels too thick, add a splash of milk until creamy and pourable.
Build the filling. In a large bowl, combine shredded chicken, 1/2 cup of the sauce, 1/2 cup cheese, cilantro, and lime juice. Add spinach or white beans if using.
Taste and adjust salt or lime.
Assemble enchiladas. Spread a thin layer of sauce on the bottom of the baking dish. Fill each tortilla with 2–3 tablespoons of the chicken mixture, roll snugly, and place seam-side down in the dish.
Top and bake. Pour remaining sauce evenly over the tortillas. Sprinkle with the remaining cheese.
Cover loosely with foil and bake for 15 minutes. Remove foil and bake 8–10 more minutes, until bubbly and lightly golden.
Finish and serve. Let rest 5 minutes. Top with extra cilantro and a squeeze of lime.
Serve with a crisp salad, steamed veggies, or brown rice.