1. Bring a large pot of water to a boil and season generously with salt. Add the spaghetti and cook until al dente. Meanwhile, place the garlic, anchovies with their oil, lemon juice, 1/4 cup olive oil, Parmesan, 1 teaspoon salt, and 1/2 teaspoon pepper in the pitcher of a blender or the bowl of a food processor and puree until smooth. Reserve.
2. When the spaghetti is cooked, scoop out and reserve 1 cup of the cooking water and drain the spaghetti in a colander. Return the cooked spaghetti to the empty pot set over low heat. Add the anchovy mixture, reserved cooking water, and parsley and stir well to combine. Season the spaghetti to taste with more salt and/or pepper if needed. Cook, stirring a couple of times, for a couple of minutes, until most of the liquid has evaporated and the pasta is glossy (the water might seem like a lot at first, but it will come together).
3. Meanwhile, if you’re cooking the eggs, heat the 2 tablespoons olive oil in a large nonstick skillet over medium-high heat. Crack the eggs into the pan and sprinkle each one with a bit of salt and a few grinds of black pepper. Sprinkle a few drops of water (like a teaspoon total) into the skillet, being sure to let the water hit the bottom of the pan, not the eggs, and immediately cover the skillet with a lid. Let the eggs cook until the whites are cooked through but the yolks are still a bit wobbly, just a minute or two.
4. Divide the spaghetti among four pasta bowls. Top each portion with a fried egg, if you cooked them, and serve immediately.

– Recipe from What Goes with What: 100 Recipes, 20 Charts, Endless Possibilities