Mix the parmesan, olive oil, egg yolks, salt, pepper, juice and the zest of lemon in a bowl. Process the basil with a little salt in a mortar to a pulp and add to the parmesan egg mixture.
Cook the pasta in salted water as usual and add some pasta water to the sauce at the end, then it will be nice and creamy.
Tip: Briefly hold the bowl with the sauce mixture over the boiling pasta water. The warmth brings out the aromas and the sauce gets a bit warm.