COOK pasta in salted boiling water, strain and reserve 2 cups water for the pan sauce.
COOK the eggs, in a nonstick pan, sunny-side up and hold warm.
SAUTÉ chopped ham in 2 tablespoons each olive oil and butter for 2 minutes in large sauté pan over high high. Add the pasta with the rest of the butter. At this point add about a ½ cup pasta water and season with salt and pepper. Cook for about 1 minute Thicken with ground pecorino cheese. Cook 1 more minute, just until coated. Add more pasta water if needed. Add a generous amount of the ground black pepper. Taste for salt.
TWIRL pasta into 4 bowls and top each serving with an egg. Garnish with chopped Italian parsley.