Place one of the oven racks in the top position of the oven and preheat the oven to 450°F.
Prick the eggplants all over with a fork and place them on a parchment-lined baking sheet. Roast the eggplants on the top rack for 50-60 minutes, turning them every 10 minutes until they are slightly charred and extremely soft. Remove the eggplants from the oven and allow them to cool.
Carefully cut the eggplants open and scoop the flesh into a blender or food processor. Add the tahini, lemon juice, garlic, salt, and parsley and pulse until well combined. Set the blender on a constant speed, then slowly drizzle in the olive oil until the mixture forms a smooth consistency.
Scoop into a serving dish and serve with the sliced vegetables.