In a medium skillet over medium-high heat, melt the butter and add the onion and diced apple. Add brown sugar and cook for 2 to 3 minutes, until onion begins to soften, stirring frequently. Add chopped fresh rosemary and parsley and mix to combine. Remove from heat. Stir in diced bread and season with salt and pepper, to taste.
Lay the chicken thighs out flat on a work surface. Cover with plastic wrap and pound with a meat mallet or rolling pin until about 1/4-inch thick. Spoon some of the apple filling into each thigh, making sure not to overstuff so you don't lose the filling while cooking. Roll up each thigh and secure with toothpicks.
Heat 2 tablespoons canola oil in a large skillet over high heat. Generously salt and pepper each side of the thighs. Place thighs in the skillet and cook for 5 minutes on each side. Remove chicken from the pan to a serving platter and let rest for a few minutes before serving.
Add potatoes to a large pot and cover with cold water. Add 1 tablespoon of salt and bring to a boil over medium heat. Reduce heat and cook until the potatoes are tender, about 15 to 20 minutes. In the meantime, add milk, butter, garlic, and rosemary sprig to a small saucepan and warm over low heat. Drain potatoes and return to the pot. Use a potato masher or large fork to mash the potatoes. Remove rosemary sprig from milk mixture and discard. Add the hot milk to the mashed potatoes. Mix to combine and season with kosher salt and freshly ground black pepper. Transfer to a serving bowl and serve with the chicken.