Whisk eggs and heavy cream together in a large mixing bowl.
Take a large nonstick pan and set over medium heat. When the pan is heated add the butter and spread out evenly over the surface of the pan. Once it starts to foam turn the heat down and add eggs. Using a spatula swirl the eggs quickly in a circular motion as you gently shake the pan back and forth to cook evenly, you don't want any color.
Once the eggs begin to set, drop the pieces of salmon, small spoonfuls of cream cheese, and green onions over the top. Season with salt and pepper, then as you slide it out onto your cutting board, roll 1 side over the top as you go to form an omelette.