In a large mixing bowl, combine the shredded chicken, softened cream cheese, 3/4 cup of the Monterey Jack cheese, Greek yogurt, green chilies, garlic powder, cumin, onion powder, salt, and pepper. Mix well until all ingredients are thoroughly blended.
Slice the zucchini lengthwise into thin strips to create tortillas. You should aim for about 12 strips.
In a 9x13 inch baking dish, spread a thin layer of chicken broth to prevent sticking to the bottom of the dish.
Take a zucchini strip, place a generous tablespoon of the chicken mixture at one end, and roll tightly. Arrange the rolled enchiladas seam-side down in the baking dish. Repeat the process until all the mixture and zucchini strips are used.
Pour any remaining chicken broth over the rolled enchiladas.
Sprinkle the remaining 1/4 cup of Monterey Jack cheese on top of the enchiladas.
Cover the dish with aluminum foil and bake in the preheated oven for 20 minutes.
Remove the foil and bake for another 10 minutes until the top is golden and bubbling.
Once done, remove from the oven and let it cool for a few minutes before serving. Garnish with fresh cilantro before serving.