Preheat oven to 400°F.
Poke holes in each eggplant with a fork, then slice them in half lengthwise.
Place on a baking sheet and brush the cut sides with olive oil.
Roast flesh-side down for 35–40 minutes, or until the eggplant is soft and collapsing.
Let cool for 20 minutes, then scoop out the flesh and discard the skins.
Transfer eggplant flesh to a blender or food processor. Add tahini, garlic confit, lemon juice, crème fraîche, cumin, and the ice cube.
Blend until smooth and creamy, about 1 minute.
Spoon into a serving bowl. Top with a drizzle of EVOO, a pinch of paprika, and smoked flaky sea salt.
Serve with endive leaves or fresh vegetables.