In a large cast-iron skillet or another oven-safe pan, melt the butter over low heat. Once melted, add the apple slices and 1/2 cup of the sugar. Stir to combine everything evenly. Cover the pan and cook gently on low heat for about 20 minutes, stirring frequently, until the apples are soft and tender.
After the apples have softened, sprinkle in the cinnamon and the remaining sugar. Increase the heat to medium-high and continue to cook, stirring frequently, for another 5-10 minutes until the apples are caramelized and coated with a rich, sweet glaze.
For an extra indulgent touch, serve the warm apples with a scoop of vanilla ice cream, if desired.