Peel squash, cut in half lengthwise and remove seeds. Cut the squash into ½-inch cubes.
In a large skillet, heat oil over medium heat (300 degrees F in an electric skillet). Add onions and cook, stirring for about 3 minutes. Add the squash, salt and chili powder.
Cover and cook, stirring every few minutes, for 10 to 12 minutes. Stir in chiles and cook about 3 minutes.
Sprinkle with cheese and cover until cheese melts, about 2 minutes. Serve hot.
Refrigerate leftovers within 2 hours.
Make your own green chiles by roasting 1 pound fresh poblano peppers (about 4 whole peppers) either by placing them over a stovetop gas flame or by roasting under an oven broiler. Turn them frequently until all sides are charred black, about 7 to10 minutes. Allow peppers to cool, about 15 minutes. Remove the stems, skins and seeds, then cut into pieces.