In a medium bowl, whisk the egg yolks with the garlic, lemon juice, white wine vinegar and mustard to mix well. While whisking, add the vegetable oil in a thin stream, followed by the olive oil, whisking continuously to emulsify. The aïoli will thicken to the texture of a silky mayonnaise. If it becomes too thick, thin it with a few drops of room-temperature water. Stir in the salt. Transfer the aïoli to a covered container and refrigerate for up to 5 days.