Split the eggplants in half through the stem and score the flesh sides. Drizzle with 1 1/2 tablespoons of the olive oil and season with salt and pepper. Roast eggplants, flesh side down on a sheet pan, until the skin begins to wrinkle and flesh is very tender, 30 to 35 minutes. Set aside to cool.
When the eggplants are cool enough to handle, scoop out the flesh and transfer to the bowl of a food processor along with the garlic, parsley, tahini, lemon juice, cumin, and cayenne and puree until smooth. Add the remaining 1/2 cup of olive oil and pulse again to incorporate. Season with salt and pepper, to taste. Transfer to a bowl and stir in the red bell pepper. Garnish with a drizzle of olive oil if desired. Serve with pita strips for dipping.
While the eggplants are cooking, make pita strips: Preheat oven to 375 degrees F. Put the pita wedges in a large mixing bowl. Combine za'atar spice mix and extra-virgin olive oil in a small bowl and drizzle over wedges. Season with salt and toss to coat evenly. Arrange pita wedges on a baking sheet and bake in the preheated oven for 10 to 15 minutes or until warmed through.