- Preheat grill to medium-high heat.
- Slice eggplants in half through the stem. Use a sharp knife to slice some deep cuts in the skin of each eggplant half and stick in a few garlic cloves.
- Drizzle the cut side of the eggplants with olive oil and season with salt and pepper.
- Grill the eggplant for about 20 minutes, flipping occasionally, until eggplant is very tender and gives easily to pressure. It should also be charred nicely all over.
- Remove eggplant and add to bowl. Cover with plastic wrap and let eggplant steam for 10 minutes.
- Scoop eggplant flesh and garlic into a food processor along with 2-3 tablespoons of olive oil, tahini, and a pinch of salt and pepper. Process the mixture until smooth.
- Transfer to serving platter with sliced veggies, warm pita wedges, and garnish baba ghanoush with paprika, sesame seeds, and fresh parsley.
Leftover baba ghanoush keeps great in the fridge for up to five days.