In a large nonstick skillet, heat oil over medium-high heat. Whisk the eggs, cream, chives, garlic salt and pepper. Add egg mixture to skillet (mixture should set immediately at edges).
As eggs set, push cooked edges toward the center, letting uncooked portion flow underneath. When the eggs are set, spoon the ham, green pepper, tomato and mushrooms over one side; on one side and sprinkle with cheeses; fold other side over filling. Invert omelet onto a plate to serve.