Preheat your grill to medium-high heat.
Wash the eggplants and pierce them with a fork to prevent them from bursting while cooking.
Place the eggplants on the grill and cook for about 15-20 minutes, turning occasionally, until the skin is charred and the flesh is soft.
Remove the eggplants from the grill and let them cool slightly. Once cool enough to handle, peel off the skin and discard.
In a bowl, mash the eggplant flesh with a fork or potato masher until it reaches a chunky puree consistency.
In a skillet over medium heat, add one tablespoon of olive oil and the minced garlic. Cook until the garlic is fragrant but not browned, about 1-2 minutes.
Add the mashed eggplant to the skillet along with cumin, coriander, and caraway. Stir to combine and cook for an additional 5 minutes to allow the flavors to meld.
Remove the skillet from heat and let the eggplant mixture cool to room temperature.
In a separate bowl, combine the plain yogurt, lemon juice, remaining olive oil, and chopped parsley. Season with salt and pepper to taste.
To serve, spread the yogurt mixture onto a serving platter, top with the eggplant mixture, and swirl together gently. Garnish with additional olive oil, parsley, and chili flakes if desired.