In a blender, purée garlic and regular olive oil until smooth. Let cool. Transfer to a food processor. Add basil, Pecorino Romano PDO, salt, pepper, and 15 grams crushed ice. With the machine running on low speed, slowly stream in grassy olive oil. Continue to process until mixture is fully emulsified. Add additional ice if needed to prevent mixture from overheating. Transfer to an airtight container and refrigerate.
In a pot over medium heat, bring salt and 2 liters water to a boil. Add pasta and cook 90 seconds. Strain, reserving pasta water, and set aside.
In a mixing bowl, combine Basil Pesto and lemon juice. Transfer 200 grams Basil Pesto to a sauté pan over medium-low heat. Add cooked pasta and 200 grams reserved pasta water. Toss until pasta is evenly coated.
Fold in stracciatella and olive oil. Season with kosher salt. Divide mixture evenly into two serving bowls. Top with sel gris, Pecorino Romano PDO, and basil leaves.
