Preheat oven to 375°F (190°C) and lightly grease a baking pan or skillet.
In a bowl, mix the brown sugar, cinnamon, and nutmeg.
Dip each biscuit in the melted butter, then roll in the sugar mixture until fully coated. Arrange the biscuits in the greased pan.
Chop the apple pie filling into smaller pieces and stir in the vanilla extract.
Spread the apple pie filling over the arranged biscuits, sprinkle any remaining sugar mixture over the top, and drizzle the remaining melted butter.
Bake for 35 minutes, or until the biscuits are golden brown and cooked through.
In a small bowl, mix the confectioners’ sugar and milk until smooth, then drizzle over the warm biscuits and serve.