Cut each sweet potato in half lengthwise, then cut each half in half widthwise. Cut each quarter into four long wedges, so you'll have a total of 32 wedges. Add wedges to a large bowl and toss with honey, 2 tablespoons olive oil and smoked paprika. Season well with kosher salt and freshly ground black pepper. Let marinate for 10 minutes, tossing twice throughout.
Preheat and oven to 425°F. Transfer the sweet potatoes to a rimmed baking sheet, and roast until they are tender and caramelized around the edges (35 - 45 minutes), tossing occasionally. You'll know they're done when a knife easily pierces the thickest part of one of the wedges.
While the potatoes are cooking, whisk together yogurt, lime juice and 1 tablespoon of olive oil. Season to taste with kosher salt and black pepper.
To serve, transfer potatoes to a large platter, and drizzle with lime yogurt (you won't use all of it). Finish with a scattering of sliced green onions and cilantro leaves.