Preheat your oven to 450°F (230°C) and position the oven rack in the upper third. Line a large baking sheet with parchment paper to prevent sticking. Slice the eggplants in half lengthwise and lightly brush the cut sides with olive oil. Arrange them on the prepared baking sheet, cut side down.
Roast the eggplants in the oven until their flesh is tender and the skin has started to collapse, around 35 to 40 minutes. If using a larger eggplant, additional time may be required. Allow the eggplants to cool briefly, then turn them over and use a large spoon to scoop out the flesh, discarding the skins.
Place the eggplant flesh in a mesh strainer set over a mixing bowl. Remove any pieces of skin that remain. Let the eggplant rest in the strainer to drain excess moisture, shaking or stirring occasionally to help release any additional liquid.
Discard the liquid in the bowl, dry it with a cloth, and transfer the drained eggplant back to the bowl. Add the garlic and lemon juice and mash the mixture with a fork until the eggplant is broken down. Mix in the tahini until it is fully incorporated. Slowly drizzle in the olive oil while stirring continuously until the mixture becomes pale and creamy.
Fold in the parsley, salt, and cumin, and adjust the seasoning with more salt or lemon juice according to your taste preference.
Transfer the baba ganoush to a serving dish. Drizzle lightly with olive oil, and garnish with additional parsley and a sprinkle of smoked paprika. Serve with your choice of accompaniments. It also makes a great spread for sandwiches!