Wash the basil leaves and place them into a food processor with the olive oil and garlic. Pulse several times until the garlic begins to break into small pieces.
Add the kosher salt and pecans and process briefly at medium speed.
Add the cheese and pulse until the cheese is mixed uniformly throughout.
Pour some or all of the pesto over the cooked pasta and mix well.
Store any remaining pesto in an airtight container in the refrigerator. It will remain fresh for a few days.