Bring a large pot of generously salted water to a rolling boil for the spaghetti.

In a deep skillet or medium pot, combine 4 cups cold water, 6 tablespoons white vinegar, and 0.25 teaspoon kosher salt for the egg poaching liquid. Bring it to a boil over high heat, then reduce the heat to low to keep it warm.

Heat a large (12-inch) skillet over medium-high heat. Add the diced bacon and cook until the fat renders and the bacon is slightly crisp, about 10 minutes. Using a slotted spoon, transfer the cooked bacon to a plate, leaving the rendered fat in the skillet.

While the bacon cooks, add the spaghetti to the boiling salted water. To the skillet with bacon fat, add the low-sodium chicken broth and simmer to reduce its volume by about one-third, which should take 8 to 10 minutes.

Cook the pasta until it is al dente, undercooking it by about 2 minutes compared to package directions (usually 8 to 10 minutes). Drain the pasta thoroughly but do not rinse.

To the reduced broth in the skillet, add the chopped baby arugula (or frisée), chopped Italian parsley, a pinch of kosher salt, and ground black pepper. Stir until combined.

Add the drained pasta to the skillet with the broth and greens. Increase the heat to high and toss vigorously to thoroughly coat the pasta with the sauce.

Continue cooking the pasta in the broth for 2 more minutes, allowing it to absorb the liquid. Remove the skillet from the heat, then stir in both the grated Parmigiano Reggiano and Pecorino Romano cheeses, tossing until well combined and creamy. Stir in the crispy bacon.

Working one at a time, carefully crack each extra large egg into a small bowl. Gently slide each egg into the barely boiling poaching liquid. Cook until the whites are set but the yolks remain runny, about 2 to 3 minutes. Use a slotted spoon to carefully lift each poached egg out of the water.

Evenly divide the Roman pasta among 4 warm serving bowls. Carefully place one poached egg on top of the pasta in each bowl. Garnish generously with fresh ground black pepper.

Serve immediately. Encourage diners to mix the egg yolk into the pasta for an even richer, creamier sauce.