Toast walnuts in 350 degree oven for 8-10 minutes, until lightly browned and fragrant. Let cool to room temperature.
Squeeze roasted garlic cloves into food processor and add toasted walnuts and a good pinch of sea salt. Pulse until mixture resembles large crumbs.
Add basil and lemon juice. With processor running, stream in olive oil. Scrape down sides and process until combined. Add additional sea salt to taste.