For the eggs in purgatory: Pulse the bread in a food processor until finely ground. Add the oregano and a pinch of salt and process until the herbs are finely chopped. Add 1 tablespoon of the olive oil and pulse until incorporated.
Heat a large nonstick skillet over medium-high heat. Add the crumbs and toast, stirring, until golden, about 5 minutes. Transfer to a bowl and stir in the Parmesan.
Wipe the skillet clean and lower the heat to medium. Add the remaining 2 tablespoons oil and the red pepper flake, garlic and onion. Cook, stirring occasionally, until softened, about 6 minutes. Add the crushed tomatoes and 1/2 cup water, cover partially and cook, stirring occasionally, until slightly thickened, about 10 minutes.
Crack one of the eggs into a small bowl. Make a small indentation in the tomato sauce in the skillet, then gently pour the egg into the indentation. Repeat with the remaining eggs. Cover the skillet and cook until the egg whites are set but the yolks are still runny, 5 to 7 minutes.
For the spicy yogurt sauce: Meanwhile, add the yogurt, oregano, cumin, red pepper flakes and lemon zest and juice to a small bowl and mix to combine. Season with salt and pepper.
Serve the eggs and sauce in shallow bowls topped with the Parmesan crumbs and spicy yogurt sauce.