Using a mix of vegetable oil and extra-virgin olive oil is crucial to the flavor of the aïoli.
Process yolks, lemon juice, garlic, salt, and pepper in food processor until combined, about 10 seconds. With processor running, slowly drizzle in vegetable oil, about 1 minute. Transfer mixture to medium bowl and, whisking constantly, slowly drizzle in olive oil. (Aïoli can be refrigerated for up to 4 days.)