Preheat the oven to 450° F.
Prep the delicata squash by removing each end with a sharp knife and then slicing each squash in half the long way. Use a spoon to scoop out and discard all the seeds from the inside of each squash. Slice each squash into half-moons 1/2-inch thick.
Line two rimmed baking sheets with parchment, and spread the squash into single even layers, using both baking sheets. Drizzle the squash with just enough olive oil to coat, and season lightly with salt. Roast the squash for about 10 minutes, then rotate the baking sheets in the oven to ensure even cooking. Roast for 10 more minutes, until the squash looks caramelized around the edges
While the squash are cooking, make the spicy yogurt dressing. Combine the yogurt with the aleppo pepper, coriander, cumin, and lime juice. Add 1 tablespoon of olive oil and a pinch or two of salt. If you are using a thick "Greek-style" yogurt, you should add 2 tablespoons of water to thin out your dressing. Taste and adjust as necessary with more salt, lime juice, or aleppo pepper.
When your squash has finished roasting, set it aside until it has cooled to room temperature. In a large mixing bowl, combine the squash with the dressing. Gently toss to coat the squash in the dressing. Taste and adjust with more salt as necessary. To serve, transfer the squash onto individual plates or a large serving platter, and garnish with the parsley and pomegranate seeds.