Brown beef and onions together. Remove from heat and drain any excess fat. Stir soup and chiles into beef mixture (right in pan--why wash more dishes?).
Spray 13x9 pan with non-stick spray. Tear several tortillas into smaller pieces (approximately into eighths), then overlap pieces to cover bottom of pan. Spread half the beef mixture across tortillas (this will be sparse), then top with 1/3 of cheese. Repeat with another layer of tortilla pieces, beef mixture and cheese.
Make a final layer of tortilla pieces to top and sprinkle with remaining cheese.