Combine the eggs, cream, Parmesan cheese, lemon zest, salt, and pepper and refrigerate for 1 hour.
Bring a pot of salted water to a boil to cook the pasta.
Meanwhile, chop the basil and toss with the lemon juice. Set aside.
When the pasta is al dente, drain and return to the pot. Stir in the eggs and cream mixture until combined. Then stir in the basil and lemon juice mixture until combined.
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