Bring water to boil in a large pan together with two tablespoons of salt.
Peel the garlic cloves, smashed them and put aside.
Chop the walnuts and add them to the bowl where you have the garlic. Season with salt and stir well. Put again a side.
Wash the basil leaves e dry them in kitchen paper. Cut them into little pieces with your hand. Add the cut basil to the bowl.
Then add the Parmesan cheese and the olive oil to the same bowl and stir well until you get a homogeneous paste. Season with pepper and let it cool outside the fridge.
When the water is boiling, drop the nests and cook for about 12 minutes.
Place the Tagliatelle all' uovo on a platter and, with a spoon, distribute the pesto evenly. Serve hot.