In a medium frying pan, heat butter over medium heat until completely melted.
Meanwhile, beat together 3 eggs with the cream or milk and salt and pepper until well combined.
Pour the egg mixture into the pan (you want the pan warmed and the butter melted but not completely hot yet).
Cover the eggs and let them cook on low-medium heat until the top JUST starts to set (slow and steady is always best for this so you don't end up crisping your bottom).
Sprinkle your shredded cheese over the almost cooked through eggs then cover the pan again and remove it from the heat completely. Let the cheese melt and eggs finish cooking off the heat.
Now once your cheese is melted, using a spatula you can fold one half of the omelette gently over the other.
To plate, you can either flip it out onto a plate OR what I do is use two spatulas to lift the omelette out and place it gently on a plate.
Top with your chives or chopped green onion and enjoy!