Preheat the oven to 400ºF. Place the sweet potatoes on a baking sheet and pierce each one several times with a fork. Rub the sweet potatoes with the olive oil and season with salt and pepper. Bake for 50-60 minutes until tender when pierced with a knife. Set aside to cool.
Heat a large skillet over medium-high heat. Add the bacon and cook until brown and crisp. Transfer to a plate. Add the broccoli and scallions to the drippings in the pan. (If there aren’t a lot of drippings in the pan, add a splash of olive oil.) Cook for about 5 minutes, stirring often, until bright green and just tender.
When the potatoes are cool enough to handle, carefully slice off the top of each potato. Scoop the sweet potato flesh into a large bowl, leaving a ¼-inch thick “shell” of flesh still intact in each potato. Add the broccoli mixture to the sweet potato flesh. Mash until thoroughly combined. Season to taste with salt and pepper. Spoon the filling back into the potato shells.
Crumble the bacon into a small bowl. Add the goat cheese and mash to combine. Crumble the bacon goat cheese over the stuffed potatoes. Return to the oven to heat through for about 10 minutes.