Preheat oven to 425°F/220°C/Gas 7.
Place the potatoes in the center of the preheated oven and bake for 50 minutes or until cooked through.
While the potatoes are baking, heat two tablespoons of olive oil and the butter in a large pan over medium heat. Once hot, add the onion and rosemary and season with salt and black pepper, to taste. Cook for 45-50 minutes, stirring occasionally until the onions are a deep, rich brown.
Deglaze the pan by adding the balsamic vinegar and gently scraping up any brown bits off the bottom with a spatula. Remove from heat and set aside.
When the cooking time is complete, remove the potatoes from the oven and transfer them to a baking rack to cool for 10 minutes or until cool enough to handle.
While the potatoes are cooling, place the caramelized onions, shredded chicken breast, and BBQ sauce in a large bowl. Stir to combine and set the bowl aside.
Once cool, cut the potatoes in half lengthwise and carefully scoop out the soft interior with a spoon, leaving a one-quarter-inch margin around the skins. (Save the cooked potato filling for another recipe).
Place the potato skins cut side down on a baking rack set over a baking sheet. Brush the skins with the remaining olive oil and return to the hot oven for 10 minutes.
Remove the baking sheet from the oven and flip over the skins with tongs. Divide the BBQ chicken and onion mixture evenly between the potato skins and top each with an equal amount of Mozzarella cheese.
Place the baking sheet back in the oven for another 10-15 minutes or until the cheese is golden brown and bubbly.
Remove from oven and garnish with fresh parsley right before serving. Enjoy!