Arrange a rack in the middle of the oven and heat to 425°.
In a large bowl, whisk together 1/4 cup of the pecorino, parsley (or basil), 1/2 tsp. of the salt, oregano, and eggs and season with black pepper. Set egg mixture aside.
Heat the oil in a 10″ nonstick ovenproof skillet over medium-high heat (make sure your handle is oven proof) Add the remaining salt, onions, and potatoes and cook, stirring occasionally, until just lightly browned and soft, about 20 minutes.
Remove skillet from heat. Add the egg mixture to the skillet and stir in to distribute the onions and potatoes evenly with the eggs.
Scatter the peppers over the top, spoon the ricotta over the mixture in 6 dollops, and sprinkle with the remaining pecorino.
Bake until lightly browned and the center set, about 15 minutes. You can check with a toothpick.
Remove from oven and run a rubber spatula around the edges of the frittata to loosen it. Let it cool slightly and then slide the frittata onto a serving plate.
Sprinkle with fresh basil if desired
Slice into wedges and serve.