Step 1

Adjust an oven rack to the middle position and heat the oven to 375 degrees. Pulse the bread in a food processor to coarse crumbs, about 10 pulses. Toss the bread with 2 tablespoons of the oil and season with salt and pepper to taste. Spread the crumbs out over a rimmed baking sheet and bake, stirring often, until golden brown, 8 to 10 minutes; set aside.

Step 2

Bring 4 quarts of water to a boil in a large pot for the pasta. Meanwhile, cook 3 tablespoons of the oil, garlic, pepper flakes, and 1/4 teaspoon salt in a 12-inch nonstick skillet over low heat, stirring constantly, until the garlic foams, is sticky, and straw-colored, 8 to 10 minutes. Transfer the garlic mixture to a small bowl and set aside. Wipe the skillet clean with a wad of paper towels and set aside.

Step 3

Stir 1 tablespoon salt and the pasta into the boiling water and cook, stirring often, until al dente. A minute or two before draining the pasta, return the skillet to low heat for 5 minutes (for the eggs). Reserve 1 cup of the pasta cooking water, then drain the pasta and return it to the pot. Stir in 1/2 cup of the reserved pasta cooking water, the garlic mixture, 3 tablespoons of the oil, Parmesan, parsley, and 3/4 teaspoon salt and toss to combine. Cover and set aside to keep warm while cooking the eggs.

Step 4

When the skillet is hot, add the remaining 2 tablespoons oil and swirl to coat the pan. Following the illustration below, quickly add the eggs to the skillet. Season the eggs with salt and pepper, cover, and cook until the whites are set but the yolks are still runny, 2 to 3 minutes. Uncover the eggs and remove from the heat.

Step 5

Loosen the pasta with the reserved cooking water as needed, then divide it into 4 individual serving bowls. Sprinkle each bowl with 2 tablespoons of the bread crumbs. Carefully slide one fried egg on top in each bowl and serve immediately, passing extra Parmesan separately.