Preheat the oven to 400°F (200°C). Scrub the sweet potatoes clean, then pierce each a few times with a fork. Bake directly on the oven rack or on a lined sheet for about 40–45 minutes, until very tender.
While the potatoes bake, steam or microwave the broccoli until just tender. If you’re short on time, you can blanch it quickly in hot water for 1–2 minutes and drain well.
When the potatoes are done, let them sit for a few minutes. Slice them in half lengthwise, scoop out a little flesh to make a shallow boat, and transfer the scooped flesh to a bowl.
Mash the potato flesh with the butter, Greek yogurt, garlic powder, and a pinch of salt and pepper until creamy. Stir in the chopped broccoli and half of the cheddar cheese.
Spoon the broccoli mixture back into the potato boats. Sprinkle with the remaining cheddar cheese.
Return to the oven for about 5–7 minutes, or until the cheese is melted and bubbling. If you like the tops a bit golden, switch to the broil setting for 1–2 minutes at the end, watching closely.
Garnish with chopped chives if using. Serve hot and enjoy the creamy, cheesy filling with a crisp potato skin.