Preheat the oven to 375°F (190°C). Lightly spray or grease a 9 x 13-inch baking dish.
In a bowl, combine the shredded chicken with 1/2 teaspoon cumin, the chili powder, and the salsa verde; mix until evenly coated.
Place about an even portion of the chicken mixture along the center of each tortilla, roll up, and arrange seam-side down in the prepared baking dish.
In a large pot over medium heat, melt the butter. Whisk in the flour and cook for 1 minute, stirring constantly.
Slowly pour in the chicken broth while whisking, and cook until the sauce thickens, about 6 minutes.
Stir in the remaining 1/2 teaspoon cumin, 1 cup of the shredded cheese, diced green chiles, sour cream, salt, and pepper. Cook, stirring, until the cheese melts and the sauce is smooth.
Pour the white sauce evenly over the arranged enchiladas, then sprinkle the remaining 1/2 cup shredded cheese on top.
Bake uncovered for 25 minutes, or until the cheese is lightly golden and sauce is bubbly.
Remove from the oven and sprinkle with the chopped cilantro before serving.