Combine first 6 ingredients and 1/4 cup cheese in a bowl; set aside.
Place a 12-inch ovenproof nonstick skillet over medium heat until hot; coat pan with cooking spray. Add ham, and cook 2 minutes or until lightly browned; remove from pan, and set aside.
Heat oil in pan over medium heat. Add onion, and cook 5 minutes or until tender. Reduce heat to medium-low; add ham. Pour egg mixture evenly over onion mixture. Cook 10 minutes or until set around edges (middle will be soft). Sprinkle with remaining 1/2 cup cheese. Remove from heat.
Wrap handle of pan with foil. Broil 4 minutes or until center is set and cheese melts. Slide gently onto a platter, and cut into 4 wedges.