This recipe takes the garlicky heat of traditional aioli (garlic mayonnaise) and dials it down to a sweet, slightly caramelized warmth. Serve it as a dip with vegetable crudités and crisp baguette toasts, with roasted fingerling potatoes, or spooned onto grilled chicken sandwiches or salmon burgers.
1Heat the oven to 375°F and arrange a rack in the middle.
2Peel any loose outer skins from the garlic head and cut off the top quarter to expose the cloves. Place the head cut-side up on a piece of foil, drizzle with 2 teaspoons of the olive oil, and wrap tightly to form a foil packet. Place on a baking sheet and bake until the garlic cloves are golden brown and very tender, about 60 to 75 minutes. Remove from the oven, open the packet, and let the garlic sit until it’s cool enough to handle. Squeeze the roasted cloves from their skins into a small bowl.
3Place the roasted garlic, mustard, and egg yolk in a food processor fitted with a blade attachment. Process until evenly combined, about 10 seconds. With the motor running, slowly add the remaining 1/2 cup olive oil in a thin stream, followed by the grapeseed or vegetable oil, until completely combined, about 2 minutes.
4Stop the processor, add the lemon juice, season with salt, and pulse until thoroughly mixed.
5Stop and scrape down the sides of the bowl with a rubber spatula, then pulse until all of the ingredients are evenly incorporated. Let the aioli sit for at least 30 minutes before using.