Preheat the oven to 350°F and generously spray a standard 6-cavity or 12-cavity donut pan with non-stick cooking spray.

In a large mixing bowl, combine the pancake mix, brown sugar, cinnamon, and nutmeg. Whisk until the dry ingredients are evenly mixed.

Create a well in the center of the dry mixture. Add the milk, egg, and melted butter. Stir until combined and a thick batter forms. Gently fold in the diced apple pieces.

Transfer the batter to a piping bag or resealable plastic bag with one corner cut off.

Pipe the batter evenly into the prepared donut cavities, filling each one about two-thirds to three-quarters full.

In a small bowl, combine the butter, brown sugar, flour, cinnamon, and nutmeg. Mix until small, pea-sized crumbs form.

Sprinkle the crumb topping over each donut cavity and lightly press it down. Bake for 10 to 12 minutes, until the donuts spring back lightly and a toothpick inserted comes out clean or with a few moist crumbs.

Allow the donuts to cool in the pan for exactly 5 minutes. Loosen the edges gently and transfer them to a wire rack to cool slightly.

Dust the donuts with powdered sugar before serving. Serve warm for the best texture and flavor.