Heat 1 tbsp olive oil in a 30 cm / 12-inch skillet over medium heat. Add the torn stale bread and toast for 3 to 4 minutes, stirring often, until deep golden. Tip into a bowl and set aside.

Bring a 6-quart / 5.7 L pot of water to a boil and salt it generously. Add the spaghetti and cook until al dente, about 9 to 10 minutes.

While the pasta cooks, wipe out the skillet, add 3 tbsp olive oil, and warm over low-medium heat. Add the sliced garlic and chili flakes and cook 1 to 2 minutes until fragrant and just turning pale gold. Don't let it brown or it turns bitter.

Stir in the chopped anchovy fillets, if using, and mash them into the oil with a wooden spoon until they dissolve, about 30 seconds.

Scoop out 1 cup / 240 ml pasta water, then drain the spaghetti. Add the pasta to the skillet with the garlic oil and toss over low heat for 1 minute, splashing in pasta water a little at a time until glossy and loosened. Stir in the parsley and half the pecorino.

Wipe the skillet clean, add the remaining 1 tbsp olive oil, and heat over medium heat. Crack in the eggs and fry for 2 to 3 minutes, until the whites are fully set and the yolks are still runny.

Divide the spaghetti among 4 bowls. Top each with the toasted pangrattato and a fried egg. Finish with the remaining pecorino and black pepper. Serve right away while the yolk is still warm.