Begin by toasting the pine nuts in a shallow pan over medium heat for about 3–5 minutes, stirring frequently until golden brown.

Bring a small pot of water to a boil and prepare an ice bath. Blanch the purple basil leaves in boiling water for 30 seconds, then transfer them to the ice bath.

In a food processor, combine the cooled pine nuts and garlic. Blend for 1-2 minutes until a smooth paste forms, adding olive oil if needed.

Add the blanched basil and remaining olive oil to the processor. Pulse until well blended, about 30 seconds.

Incorporate the grated Parmesan, salt, and lemon juice. Pulse a few times to combine without losing color.

Scoop the pesto into a serving bowl or airtight container. Store or serve fresh over pasta or as a dip.