
In a large cast-iron skillet, melt the butter over medium heat. Add the sugars, cinnamon and nutmeg, stirring until sugar is moistened. Cook until the mixture is boiling, about 2 minutes.
Add the apples and stir to coat.
Cook, stirring frequently, until the apples are cooked to desired tenderness, 6 to 10 minutes for crisp-tender and about 15 minutes for very soft apples. Serve immediately.