Preheat your oven to 375°F (190°C).
Wash and core the apples, making a wide well in the center while leaving the bottom intact.
In a bowl, combine brown sugar, granulated sugar, cinnamon, nutmeg, salt, oats, flour, and softened butter. Mix until crumbly.
Stuff each apple with the oat mixture, pressing it down gently.
Place the apples in a baking dish and pour hot water into the bottom of the dish.
Cover with foil and bake for 20 minutes, then uncover and bake an additional 25-30 minutes or until the apples are tender and the tops are golden.
Serve warm with a scoop of vanilla ice cream or whipped cream if desired.