Heat the oven to 375F. Stir the shredded chicken with the green chiles, sour cream, sauteed onion, cumin and garlic powder.
Spread a thin layer of enchilada sauce in a 9x13 dish so the bottom tortillas do not glue down.
Layer: tortilla halves slightly overlapping, half the chicken mixture, a third of the cheese. Repeat once.
Finish with a final tortilla layer, the remaining sauce spread to the edges, and the last of the cheese.
Cover with foil and bake 25 minutes, until bubbling at the edges.
Uncover and bake 10 more minutes, until the cheese browns in spots. The uncovered stage is what prevents a soggy top.
Rest 10 minutes before cutting; the layers set as it cools and the first piece comes out whole.