Preheat the broiler with rack positioned 6 inches (15 cm) from heat.
In a bowl, whisk eggs with flour, oregano, salt and pepper; whisk in cream until blended.
In a large nonstick skillet, melt butter over medium-high heat; add potatoes, mushrooms, green pepper and ham (if using); saute for 8 min or until mushrooms release their liquid and start to brown and potatoes are tender. Reduce heat to medium-low and pour in egg mixture. Cook, stirring gently with a heatproof spatula for about 2 min or until eggs are about half set. Cook without stirring for 3 min or until eggs are almost set.
Broil for about 3 min or until omelette is puffed and browned. Arrange tomatoes on top of omelette and sprinkle with cheese; broil for 1 min or until cheese is melted.