Cut the eggplant into ⅛-inch rounds. Layer and salt in a colander, place a weight, such as a plate and several cans on top, and let drain for 30 minutes. Remove and pat dry the eggplant slices.

Heat the grill to medium.

Make the dressing: Grill the bell peppers over medium-high heat, turning, until the skins are charred and the flesh is soft, 10 to 12 minutes. Let cool down slightly. Peel and seed the peppers and place them in the bowl of a food processor. Pulse and off to puree. Add the yogurt, tahini, chipotle peppers, thyme, lemon juice, salt, and pepper. Puree at high speed. Add between ⅓ and ⅔ cup water, as needed, to adjust the consistency of the dressing, which should be as dense as a thick batter. Set aside.

Place the olive oil in a medium bowl and toss in the eggplant slices. Grill over medium heat, flipping once, and remove when the slices are tender but not so soft that they disintegrate, 3 to 4 minutes per side. Brush the pita breads with the remaining oil and grill slightly to brown lightly.

Spread about 1 tablespoon of the dressing over each pita. Top with the grilled eggplant, arugula, and onion. Roll up and secure closed with a toothpick. Pour the remaining dressing into each pita roll. Wrap the bottoms if desired with waxed paper or aluminum foil, and serve immediately, with plenty of napkins.