Large globe and Italian eggplants disintegrate when braised, so do not substitute a single 1- to 1¼-pound eggplant here. You can substitute 1 to 1¼ pounds of long, slim Chinese or Japanese eggplants if they are available; cut them as directed.
Total time: 50 minutes
1. Stir tahini, yogurt, lemon juice, and water together in small bowl. Add extra water, 1 teaspoon at a time, as needed until mixture is thin enough to drizzle. Season with salt to taste and set aside. Whisk broth, pomegranate molasses, salt, and cornstarch together in medium bowl. Trim ½ inch from top and bottom of 1 eggplant. Halve eggplant crosswise. Cut each half lengthwise into 2 pieces. Cut each piece into ¾-inch-thick wedges. Repeat with remaining eggplant.
2. Heat oil in 12-inch nonstick skillet over medium heat until shimmering. Add garlic and cook, stirring constantly, until fragrant, about 30 seconds. Spread eggplant evenly in skillet (places will not form single layer). Pour broth mixture over eggplant. Increase heat to high and bring to boil. Reduce heat to maintain gentle boil. Cover and cook until eggplant is soft and has decreased in volume enough to form single layer on bottom of skillet, about 15 minutes, gently shaking skillet to settle eggplant halfway through cooking (some pieces will remain opaque).
3. Uncover and continue to cook, swirling skillet occasionally, until liquid is thickened and reduced to just a few tablespoons, 12 to 14 minutes longer. Off heat, season with salt and pepper to taste. Transfer to platter, drizzle with tahini sauce, sprinkle with almonds and parsley, and serve.