Heat a large heavy oven-safe skillet, preferably cast iron, over medium to medium-high heat. When it is hot, add the oil, and when that is hot add the onions, potatoes, oregano, salt, garlic powder and pepper. Cook, stirring occasionally, for about 15 minutes until the potatoes and onions are lightly browned and the potatoes are fork tender.
Add the greens to the skillet and sauté them for 5 minutes until they are wilted and tender.
Meanwhile, in a medium bowl, whisk together the eggs and cheese and preheat the broiler.
Pour the eggs over the potato mixture and smooth them with the back of a spatula. Cook them for 3 – 5 more minutes until the edges of the eggs start to harden.
Put the skillet under the broiler for 2 – 3 minutes until the top is browned. Remove it from the heat, allow it to cool for a couple of minutes, and using a pizza cutter, cut the frittata into 8 slices. Serve it immediately or refrigerate it for up to 3 days (this is just as delicious served cold or at room temperature as it is when it is hot).