Special equipment: a mezzaluna (a curved knife with a handle on each end), optional
For the roasted garlic: Preheat the oven to 375 degrees F.
In a ramekin, add the olive oil and garlic. Roast until the oil begins to bubble and the garlic becomes a very light golden brown, 15 to 20 minutes. Transfer the garlic to a large bowl and put half of the oil in a large pan. Reserve the rest of the oil in the ramekin for garnishing.
For the dip: In the large pan with the garlic-infused oil, add the eggplant, onion and paprika; you may have to do this in batches. Turn to medium-high heat and cook, tossing, until all sides of the eggplant are lightly golden brown, 6 to 8 minutes per batch. Transfer everything in the pan, bits and all, to the large bowl with the awaiting garlic.
Using a mezzaluna, chop the contents of the bowl until broken down but still a bit chunky. Sure you can do this in a food processor, but it may lose the texture if over-pulsed. You can also chop all of this on a cutting board, then scrape everything back into the large bowl. Add the parsley, yogurt and lemon zest and juice to the bowl. Stir to combine, taste and season with salt and pepper. Cover and refrigerate until cool.
If traveling with this to a swanky party, wait to garnish until just before serving at your host's place. Transfer the dip into a serving bowl, make a nice swirl with the back of a spoon and pour over the remaining garlic-infused olive oil. Sprinkle over the chopped parsley and serve with assorted pita chips, grissini and flatbread crisps.