Heat oven to 375'F and lightly grease a 9" square baking dish.
Toss zucchini with 1 teaspoon salt and let drain in fine-mesh strainer for 10 minutes. Squeeze the water out, using a dish towel
Heat oil in 12-inch nonstick skillet over medium heat until shimmering. Add the green onions and garlic and cook to soften, for about 2 minutes.
Stir in zucchini, cover, and cook until zucchini has released its liquid, which should take 5 - 10 minutes. Uncover and continue to cook until zucchini is dry (another minute or so) and then take off the heat.
Beat eggs, milk, and ½ teaspoon pepper together with fork in a medium sized bowl until thoroughly combined and mixture is pure yellow; do not overbeat.
Stir in zucchini mixture, feta, dill, and oregano until combined.
Transfer mixture to your prepared dish and bake until eggs are just set and edges are beginning to brown, 20 to 25 minutes.
Slice into 4 pieces, and use a flipper to plate. Can be served warm or at room temperature.