In a food processor fitted with the shredding disc, grate the zucchini. Scoop zucchini out of the bowl and onto a clean kitchen towel. Alternatively, you can use a few layered paper towels. Wrap the towel into a ball around the zucchini, hold over the sink, and wring out the excess moisture with your hands.

Replace the food processor's shredding disc with the standard chopping blade. Return the shredded zucchini to the bowl. Add garlic cloves, toasted pine nuts, basil, kosher salt, and ground black pepper. Process until smooth.

With the food processor running, add the olive oil in a slow steady stream until the pesto reaches the desired consistency. Taste and adjust seasoning as necessary.

Scoop out the pesto and fold in the grated parmesan until well incorporated. Use in your desired pasta or dinner recipe.