Peel, core, and slice the apples uniformly. Melt the butter in a large cast iron skillet set over medium heat. Place the sliced apples into the skillet, cover with a lid, and allow them to cook gently over low heat for 15 to 20 minutes, stirring regularly to prevent sticking or scorching. In a separate bowl, blend the granulated sugar, brown sugar, cinnamon, nutmeg, and salt until evenly combined. Once the apples are tender, add the sugar mixture to the skillet, stirring thoroughly to coat the fruit. Continue cooking for an additional 5 to 10 minutes until the sugars fully dissolve and create a luscious syrup. Serve the fried apples warm over generous scoops of vanilla ice cream or enjoy them on their own as a delightful side.