Place a rack in the middle of the oven and preheat to 400°. Scrub the beets well (don’t worry about peeling them) and trim their roots and stringy ends. If they’re big, cut them in halves or quarters so they’re no more than 3 in. wide at their biggest point.
In a bowl, toss the beets in the oil and 1 tsp. salt. Working with 2 or 3 beets at a time, wrap them in foil and tightly crimp the edges to make small packets. Lay the packets side by side on a rimmed baking sheet and roast until you can pierce them easily with a fork, 40 to 50 minutes. Let the beets cool in their packets.
When the beets are cool enough to handle, remove them from the foil and rub off the skins; they should peel off without much resistance. Cut the beets into 1-in. wedges.
In a large bowl, whisk together the tahini, ice water, lemon juice, yogurt, and 1⁄2 tsp. salt. The mixture may seize up at first, but keep whisking and it will smooth itself out. Season with the Aleppo pepper and coriander, then stir in the beets and dill. Garnish with a few parsley leaves if you like.