Preheat a 6-8" non-stick pan to medium heat. Add olive oil. When oil smokes slightly, add butter then add the eggs as soon as the butter melts. Using a high heat silicone spatula, push the cooked egg from the edges of pan toward the middle. When most of the egg is cooked, use the spatula to flip the omelette over. Add cheese and smoked salmon. Remove the omelette from the pan and "fold" onto a serving plate. Garnish with sliced tomato and green onion. Enjoy with potatoes, grits or any other brunch side. This recipe also works well as an egg white only omelette.