Center a rack in the oven and preheat it to 425 degrees F. Line a baking sheet with parchment paper.

Whisk the cider vinegar, paprika, salt, cumin, and cayenne together. When the spices are dissolved, whisk in the oil and honey and taste for cayenne.

Arrange the carrots on the baking sheet, pour over about 1⁄3 cup of the spice syrup you just made and turn the carrots until they’re evenly coated. Set the remaining syrup aside.

Roast the carrots for 20 minutes, then flip them over, rotate the baking sheet and roast for another 20 to 30 minutes, until they are tender and browned — they might be a tad charred here and there and they’ll probably be a bit wrinkled, and it’s all good. (The carrots can be made ahead to this point and kept at room temperature for up to 6 hours.)

Stir a tablespoon of the leftover syrup into the yogurt, taste and add more, if you’d like. (The yogurt sauce can be covered and refrigerated for up to 2 days.) Serve the carrots hot with the yogurt sauce spooned over them or spread under them as a base. Alternatively, cover the sauce and refrigerate it, then serve as a dipping sauce with the room-temperature carrots.

WORKING AHEAD: You can make the carrots up to 6 hours ahead and keep them at room temperature; the yogurt sauce can be made and refrigerated up to 2 days in advance.