Pappardelle with Bagna Cauda, Radicchio and a Fried Egg

1/4 c extra-virgin olive oil
15 anchovy fillets
8 large garlic cloves, minced
1/4 c finely chopped flat-leaf parsley
12 radicchio leaves, torn into small pieces
Grated zest and juice of half a lemon
Kosher salt
Freshly ground black pepper
8 ounces egg pappardelle

For finishing the dish:
1/4 c extra-virgin olive oil
4 large eggs
Parmesan cheese
1 heaping T finely chopped flat-leaf parsley

To make the bagna cauda, place a large skillet over medium-high heat. Add the olive oil, anchovies and garlic and cook, breaking up the anchovies with a fork and stirring constantly, until the anchovies dissolve and the garlic is soft and fragrant, about 2 minutes. Turn off the heat, stir in the parsley, radicchio and lemon zest and juice. Season to taste with salt and pepper.

Prepare the pasta by bringing a large pot of water to a boil over high heat. Add enough kosher salt until the water tastes salty and return to a boil. Add the pasta and cook, stirring occasionally, until al dente.

To finish the dish, heat the olive oil in a large nonstick skillet over high heat until the oil is almost smoking, about 2 minutes. Break 1 egg into a small bowl and pour into the skillet. When it just begins to set around the edges, break the second egg into the bowl and pour into the skillet. (By waiting a moment before adding the next egg, the eggs won’t stick together.) Repeat with the remaining 2 eggs. Cook until the edges are golden, the whites are set and the yolks are still runny.

Use tongs to lift the pasta out of the water and transfer it quickly, while it’s dripping with water, to the skillet with the bagna cauda. Place the skillet over high heat. Toss the pasta to combine the ingredients and cook for 1 to 2 minutes more.

Using tongs, divide the pasta among 4 plates, twisting it into mounds. Grate a generous layer of cheese over each. Place an egg over the cheese. Sprinkle the parsley over the pasta and serve with more grated cheese and pepper.