Add the basil, Parmesan, pine nuts and garlic to a food processor. Pulse a few times to break up the garlic and nuts. Add 1/4 cup of the olive oil and pulse a few more times. Scrape down the sides as needed. With the motor running, stream in the remaining 1/4 cup olive oil and the lemon juice until a thick paste forms. Add salt and pepper to taste and pulse a few more times to combine.
Remove and store in an airtight container for up to 2 days (with a thin layer of olive oil over the top so that it does not turn brown).
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