Preheat the oven to 400°F. Line a baking sheet with parchment paper.
Prick the sweet potatoes several times with a fork and place them on the baking sheet. Bake for 45–50 minutes, until very tender when pierced with a knife.
While the potatoes bake, combine the shredded chicken, barbecue sauce, smoked paprika, and garlic powder in a small saucepan. Warm over medium-low heat for 5 minutes, stirring occasionally.
In a small bowl, stir together the Greek yogurt, lime juice, and a pinch of salt.
Slice each baked sweet potato open lengthwise and gently fluff the insides with a fork. Season with salt and pepper.
Fill each potato with BBQ chicken and top with cheddar, if using. Return to the oven for 3–4 minutes to melt the cheese.
Finish with a drizzle of the yogurt sauce, extra barbecue sauce, and sliced green onions. Serve warm.