Preheat the broiler.
In a large, broilerproof 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 throughout the egg. Use a wooden spoon or rubber spatula to spread the onion in the pan throughout the egg. 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.
Excerpted from The Covenant Kitchen by Jeff and Jodie Morgan. Copyright (c) 2015 by Jeff Morgan and Jodie Morgan. Excerpted by permission of Schocken, a division of Random House LLC. All rights reserved. No part of this excerpt may be reproduced or reprinted without permission in writing from the publisher.