Basil Pesto

1 cup packed fresh basil leaves
1 cloves garlic
1/4 cup pine nuts
1/3 cup extra-virgin olive oil, divided
Kosher salt and freshly ground black pepper, to taste
1/3 cup freshly grated Parmesan cheese 

Combine the basil, garlic, and pine nuts in a food processor and pulse until coarsely chopped. Add the oil and process until fully incorporated and smooth. Season with salt and pepper.