Melt the butter in a large skillet over medium heat. Add the apples and stir gently so the slices become coated without breaking.
Sprinkle brown sugar, cinnamon, nutmeg, and salt over the fruit. Cook for 3 to 4 minutes, stirring occasionally as the sugar begins to melt.
Pour in the lemon juice and most of the apple juice. Lower the heat slightly and cover the skillet for 5 minutes.
Remove the lid and check the texture. The apples should be tender around the edges but firm enough to hold their shape.
Stir cornstarch into the remaining apple juice, then pour it into the skillet. Cook for 1 to 2 minutes until the sauce looks glossy and lightly thickened.
Remove the skillet from the heat and let the apples stand briefly. Serve warm, spooning the cinnamon sauce from the pan over every portion.
