1. Whisk together the oil, cheese, lemon juice, salt & pepper. Can be made up to 8 hours ahead. Bring to room temperature before using.
2.. Prepare spaghetti according to package directions. Drain, but reserve 1 cup of spaghetti-water.
3. Toss the spaghetti with the lemon sauce and zest. Add spaghetti water, if needed, to moisten slightly.
4. Transfer to serving platter; top with basil, coarse salt and freshly ground pepper. Serve with lemon wedges.
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