Preheat the oven to 190°C (375°F) and line a 12-cup muffin tray with paper liners or lightly grease it.
In a medium bowl, whisk together flour, baking powder, cinnamon, and salt.
In a separate large bowl, whisk melted butter with both sugars until smooth. Add eggs and vanilla, mixing until combined.
Gradually stir in the dry ingredients, alternating with milk, just until the batter comes together. Do not overmix.
Fold in the diced apples gently with a spatula, distributing them evenly through the batter.
Divide the batter evenly among the muffin cups, filling each about three-quarters full. Sprinkle the tops with turbinado sugar if desired.
Bake for 18–22 minutes or until a toothpick inserted in the center comes out clean. Let cool slightly before removing from the pan.