Place the walnuts in a dry skillet over medium heat. Stir and flip the nuts frequently for 3-4 minutes until the nuts are fragrant and lightly browned. Transfer to a plate and let cool fully.

Add the cooled walnuts to a food processor. Add the basil, parsley, oregano, garlic, lemon zest, lemon juice, black pepper, and salt. Pulse several times until the mixture is finely chopped and forms a coarse paste. Scrape down the sides of the bowl as needed so the mixture processes evenly.

With the machine running, slowly pour in the olive oil in a steady stream so the mixture emulsifies and becomes smooth.

Add the ice and process again until the sauce loosens to a spoonable consistency. Taste and tweak the seasoning if needed.