Preheat oven to 350 degrees F (175 degrees C). Grease a 2-quart casserole dish.
Combine cooked rice, turkey, evaporated milk, Monterey Jack cheese, Cheddar cheese, mixed vegetables, onion, chopped green chiles, eggs, cilantro, and butter in a large bowl, stirring until thoroughly mixed.
Pour into prepared casserole dish.
Bake in the preheated oven until casserole is set and top is golden brown, 45 to 50 minutes.