To Make Aoili
- Smash garlic cloves into a paste using the side of a large, heavy knife.
- Whisk together yolk, lemon juice, and mustard in a small bowl. Combine oils. In small increments, add oils to the yolk mixture. Whisk constantly until all the oil is incorporated and the mixture is emulsified.
- Whisk in garlic paste and season with salt and pepper. If aioli is too thick, whisk in a couple drops of water. Chill, covered, until ready to use.
To Grill Vegetables
- Set the charbroiler to high heat and allow to preheat for 5 minutes.
- Toss the vegetables with olive oil, salt, and pepper.
- Grill a few pieces at a time, cooking until just charred but still retaining a bite. Serve alongside garlic aioli.