Toast garlic in a small, dry skillet over medium heat, shaking pan occasionally, until garlic is softened and spotty brown, about 8 minutes. When cool, remove and discard skins.
In a food processor, pulse toasted garlic, olives, shallot, basil, parsley, anchovy (optional), Parmesan, olive oil and 1 tbs lemon juice, stopping as necessary to scrape down sides of the work bowl. Transfer mixture to a small bowl and add salt and pepper to taste.
Bring 4 quarts of wter to a rolling boil in a stock pot. Add 1 tablespoon of salt and the pasta, stiring to separate and kook until al dente. Drain, reserving 1/2 cup cooking water and return pasta to stock pot.
Stir 1/4 cup of the pasta cooking water into pesto and then stir pesto into pasta. Toss, adding more pasta cooking water as needed.
Serve immediatley, with lemon sedges and extra Parmesan at the table.
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