**Prepare the Apple Filling:** In a small saucepan, melt the butter over medium heat. Add the diced apples, brown sugar, cinnamon, nutmeg, and water. Cook, stirring occasionally, until the apples soften and the mixture thickens, about 8-10 minutes. Remove from heat and let cool.
**Make the Biscuit Dough:** In a mixing bowl, combine the flour, baking powder, and salt. Cut in the cold butter using a pastry cutter or your fingers until the mixture resembles coarse crumbs. Gradually stir in the milk until a dough forms.
**Assemble the Biscuits:** On a floured surface, roll out the dough into a rectangle about 1/2-inch thick. Spread the cooled apple filling evenly over the dough. Roll the dough up tightly, starting from a long edge. Slice into 1-inch rounds.
**Bake the Biscuits:** Place the rounds on a parchment-lined baking sheet. Bake in a preheated oven at 375°F (190°C) for 15-18 minutes, or until golden brown.
**Add Topping:** While the biscuits are still warm, brush with melted butter and sprinkle with the cinnamon-sugar mixture.
**Serve:** Let cool slightly and enjoy warm!