Preheat the oven to 375°F (190°C) and line a 12-cup muffin tin with paper liners.
In a large mixing bowl, whisk together the flour, baking powder, cinnamon, nutmeg, and salt.
In a separate medium bowl, whisk the melted butter, granulated sugar, and brown sugar until smooth. Add the eggs, milk, and vanilla extract, whisking until well incorporated.
Gently fold the wet ingredients into the dry ingredients until just combined; do not overmix.
Fold the diced apples into the batter using a spatula.
Distribute half of the batter among the muffin cups. Spoon 1 teaspoon of caramel sauce onto the center of each, then cover with the remaining batter.
Bake for 18 to 22 minutes, or until a toothpick inserted into the muffin portion comes out clean.
Allow muffins to cool in the pan for 5 minutes, then transfer to a wire rack. Drizzle with additional caramel sauce before serving.