In a small saucepan, cover the garlic with vegetable oil. Bring to a simmer over medium heat and cook for 15 to 20 minutes until lightly golden. Remove from the heat and add the thyme and rosemary. Let cool completely, then discard herbs.
Transfer the cooled oil and garlic to a quart container with the lemon juice, mustard, egg yolk, salt, and pepper. Blend with an immersion blender, starting at the bottom and working up, until a thick mayo forms. Transfer to an airtight container and store in the fridge for up to one week.
