4 large eggs
½ cup distilled white vinegar
8 oz. dried spaghetti
Vegetable or peanut oil, for frying
½ cup pork jowls, diced
1 garlic clove, minced
¼ cup chicken broth
1½ cups heavy cream
1 cup all-purpose flour
1 cup buttermilk
1 cup panko breadcrumbs
Kosher salt and freshly ground black pepper
2 tsp. thinly sliced fresh flat-leaf parsley
1 Tbsp. fresh lemon juice
½ tsp. red pepper flakes
Fill a wide 2-quart saucepan with about 4 inches of water. Add the vinegar and bring the water to just below simmering. Prepare a bowl of ice water. Crack each egg into a small cup and slip it into the hot water; cook until the whites are just set, about 3 minutes. Use a slotted spoon to transfer the eggs to the ice water. Transfer the cooled eggs to a shallow dish lined with paper towels (or a dish towel) and refrigerate for 30 minutes.
Bring a large pot of salted water to a rolling boil. Add the pasta and cook according to package directions, until al dente but not mushy; drain the noodles in a colander.
Meanwhile, heat 4 inches of oil in a medium pot to 350 degrees.
In a large skillet (separate from your frying pot), cook the pork jowls over medium-high heat, turning as needed until their fat has rendered and they are just starting to crisp, about 6 minutes. Add the garlic and cook for 1 minute. Pour in the chicken broth and heavy cream and simmer to reduce until the sauce is thick enough to coat the noodles, 5 to 6 minutes.
Put the flour, buttermilk and panko in separate wide, shallow bowls. Dredge the eggs in flour. Gently shake off the excess and dip in the buttermilk and then coat in the breadcrumbs.
Deep-fry the eggs until nicely browned but still soft in the middle. Transfer to a paper towel, season with salt and pepper, and reserve.
Add the pasta to the sauce and toss to coat. Finish with the parsley, lemon juice, and salt and pepper to taste. Toss until combined and heated through. Divide the pasta among serving plates, sprinkle with a pinch of red pepper flakes, and top each with a fried egg.