How to Make It
Make the pasta In a food processor, pulse the 1 3/4 cups of flour with the salt. In a medium bowl, beat the egg yolks with the whole egg and olive oil. Add to the flour in the food processor and pulse until the dough just comes together. Transfer to a lightly floured work surface and knead until very smooth but stiff, 5 to 10 minutes. Cover with plastic wrap and let stand at room temperature for 1 hour.
Divide the dough into 4 pieces and work with 1 piece at a time, keeping the rest covered. Press the dough to flatten it. Using a pasta machine set at the widest setting, run the dough through successively narrower settings until you reach the sixth one. Cut the pasta sheet into a 10-inch length, lay it on a lightly floured work surface and generously dust with flour. Repeat with the remaining dough.
Loosely roll up the pasta sheets and then, using a very sharp knife, cut them into scant 3/4-inch-wide ribbons. Transfer the pappardelle to a large baking sheet and gently toss with more flour. Let stand at room temperature for 30 minutes.
In a large pot of salted boiling water, cook the pasta until al dente, 2 to 3 minutes. Drain, reserving 1 cup of the cooking water.
Meanwhile, make the carbonara In a large bowl, beat the egg yolks with the whole egg, the cheese, lemon zest, 1/2 teaspoon of salt and 1 teaspoon of pepper. Very gradually whisk in 1/2 cup of the reserved hot pasta water to temper the eggs. Add the pasta and half the caviar and vigorously toss until hot and creamy, 1 to 2 minutes. Transfer to bowls and top with snipped dill and dollops of the remaining caviar.