Heat broiler to high with rack 6 to 8 inches from heat. Place eggplants on a foil-lined baking sheet and broil, turning every 5 to 10 minutes until charred and soft, 15 to 25 minutes total, depending on your broiler. Let cool. Trim off stem, peel and discard skin. Set aside.
Heat oven to 400ºF for the veggies.
Toss the onion, sweet potato and cauliflower together in a large bowl with 3 tablespoons olive oil, 2 teaspoons zaatar and ¾ teaspoon salt. Combine the zucchini and yellow squash in another bowl and toss with 1 tablespoon olive oil, remaining 1 teaspoon of zaatar and ¾ teaspoon salt. Arrange veggies on two separate baking sheets.
Roast veggies, rotating racks after 15 minutes until caramelized and tender, 25 to 30 minutes for the zucchini and yellow squash, 35 minutes for the sweet potatoes and cauliflower. Remove from oven and set aside.
Make the baba ganoush: In a food processor, combine the olive oil, pomegranate juice, tahini, yogurt, garlic, and salt. Process until well combined, about 30 seconds. Add the peeled eggplant and process or pulse until almost smooth, leaving a little texture. Stir in the fresh pomegranate arils IF USING.
Serve the baba ganoush on a platter or in a large bowl. Top with the roasted veggies, pistachios, extra zaatar, parsley, and ½ cup pomegranate arils.
Notes
You can make the baba ganoush up to a day in advance. Store airtight in the fridge until ready to serve.