Preheat the oven to 425°F (220°C). Pierce the eggplants several times with a fork and place them on a lightly oiled baking sheet.
Roast the eggplants for 35 to 40 minutes, turning them once halfway through, until the skins are deeply browned and the flesh is very soft and collapsed. For a smokier flavor, you can char the eggplants over an open flame instead.
Let the roasted eggplants cool enough to handle, then cut them open and scoop the flesh into a colander. Let the excess liquid drain for about 10 to 15 minutes so the dip does not become watery.
Transfer the drained eggplant to a mixing bowl and gently mash it with a fork until mostly smooth while keeping a little texture.
Add the tahini, lemon juice, garlic, Greek yogurt if using, olive oil, cumin, sumac, smoked paprika, salt, and black pepper. Stir gently with a wooden spoon or fork until everything is well combined.
Taste the baba ganoush and adjust the lemon juice, salt, or spices according to your preference. Cover and refrigerate for 30 minutes to allow the flavors to develop.
Transfer the dip to a serving bowl, spread it into a shallow swirl, and drizzle with olive oil. Garnish with parsley, toasted pine nuts, and a light sprinkle of sumac or smoked paprika before serving.