How to Make It
In a large saucepan, combine the apples with the wine, water, sugar, ginger, cinnamon stick and 1 tablespoon of the butter and bring to a simmer. Cover and cook over moderately low heat, stirring occasionally, until the apples are tender, about 12 minutes. Uncover and cook, stirring, until the liquid is nearly evaporated, about 5 minutes longer. Discard the ginger and cinnamon stick.
In a large skillet, heat the olive oil until shimmering. Season the pork medallions with salt and pepper. Add them to the skillet and cook over high heat, turning once until browned, about 10 minutes. Transfer the pork to a plate and keep warm.
Return the skillet to high heat and add the remaining 2 tablespoons of butter and the rosemary. Cook, stirring, until the rosemary browns and the butter is fragrant, about 2 minutes. Discard the rosemary sprig. Spoon the applesauce onto plates and top with the pork. Spoon the rosemary butter over the top and serve.