Place eggs in medium saucepan; cover with cold water. Bring to a boil. Reduce heat; simmer about 15 minutes.
Immediately drain; run cold water over eggs to stop cooking. Peel eggs. Cut tips off both ends of each egg to create a flat surface for eggs to stand on. Cut each egg in half crosswise.
Remove yolks; place in small bowl and mash. Add onions, cilantro, chile, mayonnaise and mustard; blend well.
Spoon about 1 tablespoon yolk mixture into each egg half. Top each with cheese. Sprinkle with chili powder. Cover; refrigerate at least 1 hour or until serving time.