Step 1

Bring a large pot of generously salted water to a boil.

Step 2

In a deep skillet or medium pot, egg-poaching liquid to a boil over high heat, then leave on low heat.

Step 3

Heat a large (12-inch) skillet over medium-high heat, cook bacon until fat renders and meat is slightly crisp, about 10 minutes. Set aside with a slotted spoon and transfer to a plate, leaving the fat in the skillet.

Step 4

At the same time, add the pasta to the salted water, and add the broth to the bacon fat and simmer the broth to reduce by 1/3, about 8 to 10 minutes.

Step 5

Cook the pasta until al dente, under-cooking by 2 minutes, about 8 to 10 minutes. Drain pasta but do not rinse.

Step 6

To the broth add the arugula, parsley and 1/4 teaspoon salt and black pepper.

Step 7

Add drained pasta, raise heat to high, and toss to coat with sauce.

Step 8

Finish cooking the pasta in the broth for 2 minutes, then remove from heat, stir in cheese, and toss. The spaghetti will soak up any liquid.

Step 9

Working one at a time, carefully crack each egg into a small bowl and very gently slide into barely boiling poaching liquid. Cook until whites set but yolks are still runny, about 2 to 3 minutes. Using a slotted spoon, lift each egg out of the water.

Step 10

Evenly divide pasta between 4 warm bowls. Place each egg atop each bowl of pasta. Top generously with black pepper.

Step 11

Serve immediately, mixing up the pasta to spread the egg and yolk throughout the bowl.