Preheat the oven to 350 degrees. Coat a baking sheet pan with cooking spray.
Add ¾ cup warm water to the broken matzo and toss. Allow to sit 3-5 minutes, until the water is absorbed
Beat 4 of the eggs lightly with a fork, stir in ¼ teaspoon salt and the pepper, and add to the matzo. Toss the mixture well, and then occasionally for the next 5 minutes to allow some of the egg to be absorbed.
Meanwhile, toss the arugula with 1 tablespoon of the oil, the vinegar, and the remaining 1/8 teaspoon salt.
Heat 1 tablespoon of the oil in a large nonstick skillet over medium heat. Add the matzo mixture and press it lightly into an even disc in the pan. Cook until the bottom is browned and the mixture holds together well when you shake the pan, about 5 minutes. Place the sheet pan (sprayed side down) over the skillet and invert the rosti onto the pan. (The browned side will face up.) Spread the top evenly with the ricotta and place in the oven for 5 minutes.
Meanwhile, heat the remaining 1 tablespoon olive oil in the skillet. Crack the remaining 4 eggs in the skillet and cook them, sunny side up, until the whites are just cooked through and the yolks still runny, about 3 minutes.
Cut the rosti into four wedges and place each on a plate. Top with the arugula and then an egg; sprinkle with the feta and serve immediately.
Recipe Notes
428 calories, 23 g protein, 27 g carbohydrates, 1 g fiber, 8 g saturated fat, 602 mg sodium