How to Make It
Preheat the broiler.
In a large, broiler-proof skillet, heat the olive oil over medium heat. Add the onion and green onions and sauté until the white onion is translucent, 3 to 4 minutes.
Meanwhile, crack the eggs into a large bowl and whisk to blend thoroughly. Stir in the salmon.
Reduce the heat to medium-low, push the onion to the edge of the skillet, and pour in the egg/salmon mixture, making sure the salmon is evenly distributed amid the egg. Use a wooden spoon or rubber spatula to spread the onion in the pan. Lay the cheese slices evenly across the top of the egg. Garnish with the oregano. Cook until the bottom of the egg has set, 3 to 5 minutes. The top of the frittata should still be runny.
Transfer the skillet to the top oven rack directly under the broiler. Cook the frittata until the top sizzles and takes on a golden brown hue, 3 to 5 minutes.
Remove the pan from the oven, cut the frittata into quarters, and serve immediately with freshly ground pepper to taste.