In a bowl, whisk together the eggs and 1/2 tsp. of the salt. Set aside.
In the deep half of a frittata pan over medium heat, melt 1 Tbs. of the butter. When it foams, add the zucchini and sprinkle with the remaining 1/2 tsp. salt. Sauté for 30 seconds. Add the oregano and the 2 tsp. parsley and cook for 30 seconds.
Add the eggs and, using a rubber spatula, quickly and lightly stir the eggs in a small circular motion to combine them with the zucchini. Using the spatula, gently lift the cooked edges to allow the uncooked eggs to flow underneath. Sprinkle the cheese on the frittata; do not stir. Reduce the heat to low and cook, without stirring, 4 to 5 minutes more.
Meanwhile, in the shallow half of the frittata pan over medium heat, melt the remaining 1/2 Tbs. butter. Place the shallow pan upside down on top of the deep pan and flip the frittata into the shallow pan. Reduce the heat to low and cook, covered, for 3 minutes. Remove the top pan and continue cooking until the eggs are set, about 5 minutes more.
Using the spatula, loosen the edges of the frittata and gently slide it onto a plate. Garnish the frittata with parsley. Serve with the arugula salad. Serves 8 to 10.
Go to full version of