Prep the garlic: Slice the top off the head of garlic to expose the cloves.
Drizzle with 1 teaspoon olive oil and wrap tightly in foil. If using loose cloves, keep them in their skins, toss with oil, and wrap in foil.
Air-fry the garlic: Place the foil packet in the air fryer basket. Cook at 370°F (188°C) for 15–18 minutes, until cloves are soft and lightly caramelized.
Let cool until safe to handle.
Squeeze and mash: Squeeze the roasted garlic out of the skins into a small bowl. Mash into a smooth paste with a fork. You’ll need about 1–2 tablespoons of paste, depending on how garlicky you like it.
Start the base: In a medium bowl, whisk the egg yolk, Dijon, lemon juice, salt, and pepper until smooth and slightly thickened.
Emulsify: While whisking constantly, slowly drizzle in the neutral oil, a few drops at a time at first.
Once it starts to thicken, you can add the oil in a slow, steady stream. The mixture should become creamy and glossy.
Add the flavor: Whisk in the extra-virgin olive oil for richness, then fold in the roasted garlic paste. Taste and adjust with more lemon juice, salt, or pepper.
Add a pinch of cayenne or smoked paprika if you like a little heat.
Chill and serve: Cover and refrigerate for at least 20 minutes to let the flavors meld. Serve with fries, grilled chicken, roasted vegetables, or as a spread for burgers and sandwiches.