Prep the Apples: Peel the apples (if desired) and remove the cores. Cut the apples into 1/4-inch slices.
Season the Apples: Transfer the apple slices to a large food storage bag or bowl. Add the brown sugar, cinnamon, nutmeg, and salt; toss to coat the apple slices.
Cook the Apples: Melt the butter in a large skillet over medium heat. Add the apple and sugar mixture. Cook the apples, stirring occasionally, for about 7 to 10 minutes or until they are tender. Add the vanilla and stir to blend.
Serve: Transfer the cooked apples to small serving bowls and serve with a dollop of whipped cream or sprinkle with cinnamon sugar.
Notes
For a thicker syrup, whisk a scant teaspoon of cornstarch and 1 tablespoon of water in a small bowl to make a slurry. Add the slurry to the apples about 2 minutes before they're done.