Preheat oven to 350 degrees. Lightly grease a 9x13 inch baking dish. Place cooked, shredded chicken in a large bowl.
In a large skillet, heat oil over medium heat. Saute onions and garlic until soft, 3-5 minutes. Add spinach and saute a few minutes more until wilted. Stir spinach mixture into chicken, along with 1/2 cup of the cheese.
To the same skillet, melt the butter. Stir in the flour. Whisk in the chicken broth and bring to a simmer. Stir in the cumin and season with salt and pepper to taste.
Cook until broth is thickened, then stir in the green chiles, sour cream and lime juice. Stir 1 cup of the sauce to the chicken and spinach mixture.
Spread about 1/3 cup of the sauce in the bottom of the prepared pan. Divide the chicken mixture between the tortillas and roll up tightly. Place seam side down in the pan.
Pour remaining sauce over the enchiladas and sprinkle with the remaining cheese. Cover with foil and bake for about 20 minutes. Uncover and bake 10-15 minutes more, or until cheese is bubbly and enchiladas are golden brown. Garnish with fresh chopped cilantro, if desired.