Mix flour, egg, yolks, half the oil, and salt in a bowl to form a rough paste.
Knead the dough on a floured surface until smooth and rest for 15 to 30 minutes.
Roll the dough through a pasta machine until 1mm thick and cut into 15cm squares.
Grind basil, salt, pine kernels, and garlic in a mortar into a fine pulp.
Incorporate olive oil and parmesan into the herb pulp until the pesto is smooth.
Boil the pasta sheets in salted water with a dash of oil for three minutes.
Gently warm a few spoons of pesto with some pasta cooking water in a large pan.
Toss the cooked pasta sheets into the pesto sauce and serve garnished with basil.