In a small saucepan, combine olive oil and garlic cloves. Cook over low heat, stirring occasionally to prevent burning, until the garlic turns light golden brown and tender, about 15 minutes.
Carefully remove from heat. The oil will be very hot. Once the oil has cooled to room temperature, remove and reserve the garlic cloves. Keep the garlic-infused oil, you will need it soon.
Meanwhile, warm a skillet over medium heat. Add the pistachio nuts to the skillet. Stir them continuously over medium heat until they are toasted and fragrant. Remove from heat.
Add toasted pistachios to a food processor along with room temperature garlic infused olive oil, roasted garlic pieces, fresh mint and basil, parmesan or pecorino cheese, fresh lemon juice, and lemon zest.
Pulse the mixture, scraping the sides periodically, until the mixture is creamy but still has a nutty texture.
Scrape the pesto into a bowl and taste. Stir in salt to taste if needed.
Stir in additional olive oil for texture if desired.
Serve as a sauce, condiment, or topping, or use as a marinade depending on your preference.
