Roast the eggplant using the method that works best for your kitchen: You can place the eggplant directly on a gas burner turned to medium-high heat and cook, flipping it frequently, until it is charred on all sides and tender inside, about 20 minutes. (Lay a few strips of foil around the burner for easy cleanup.) Or char the eggplant skin under a hot broiler, turning the eggplant frequently, and then finish roasting it until tender on a baking sheet in a 450°F oven. Remove the eggplant from the heat and let it rest until cool enough to handle.

Halve the eggplant lengthwise and scoop the eggplant flesh into a blender. Discard the skin and stem.

Add the egg yolk to the blender and pulse until well combined. Add the vinegar, salt, and pepper and blend for another few seconds. With the motor running, slowly stream in the mild olive oil and blend until the mixture is thick and creamy. Taste and adjust the seasoning with more vinegar, salt, and pepper if needed.

Transfer the dip to a small serving bowl, garnish with the cilantro sprigs, and drizzle lightly with olive oil. Serve at room temperature.