For the pasta kerchiefs:
1 2/3 cups plus 1/2 cup all-purpose flour (for dusting)
2 egg yolks
1 tbsp kosher salt
1 tbsp extra virgin olive oil
For the rest of the dish:
1 tbsp white vinegar
8 tablespoons unsalted butter
8 slices smoked cured jambon de Paris or other lightly smoked, dry-cured ham
3/4 cup shaved Parmigiano-Reggiano cheese
4 tablespoons pine nuts, toasted
Best quality balsamic vinegar, for sprinkling
Coarsely ground black pepper
1. Place flour in a food processor, turn it on and add 2 egg yolks and 1 egg one at a time through feed tube. Mixture should have consistency of moist cornmeal. Transfer to a large mixing bowl. Have 1/2 cup cold water ready. Add salt and olive oil; mix with your hands, squeezing dough through your fingers. Add cold water a little at a time, until a smooth dough forms; it should be between soft and stiff. Knead 10 minutes then let rest, dusted with flour and covered with an overturned bowl for 2 hours.
2. Using a pasta machine without cutting blades, roll dough first on largest setting, folding it in half and decreasing the machine setting each time through, working your way down to the thinnest setting, so that the sheets are 5 to 6 inches wide. It should get soft and silky without shredding on edges. Cut sheets about 10 inches long. Reroll any scraps. (This will make about 8 sheets, but you will only need 4; reserve extra for another use.)
3. Bring a large pot of salted water to a boil. Meanwhile, fill a medium pan with 2 inches of water and vinegar; bring to a simmer. Gently crack 4 eggs into it and poach until whites are just set. Have 4 bowls ready, and using a slotted spoon, place one egg in each bowl and set aside in warm place. Discard egg-cooking water; add butter to same pan. Cook over medium heat until it begins to smell nutty and turn brown. Set aside.
4. Place 2 slices of ham in boiling water for 10-20 seconds, just long enough to heat through. Remove with slotted spoon or kitchen tweezers or chop sticks, shaking off the excess water, and place in bowl next to the poached egg. Repeat with remaining ham. Add 4 pasta sheets to boiling water and cook for about 90 seconds, until cooked through. Remove each sheet of pasta from the boiling water and gently transfer each to a serving bowl, laying it over the egg and ham like a sheet. The pasta should form a package over the ham and egg. Quickly reheat butter and spoon a little over each bowl of pasta, followed by a little balsamic vinegar. Sprinkle with shavings of cheese and pine nuts. Season with salt and pepper.