Preheat the oven to 350°F (175°C). Grease an 8-inch (20 cm) square baking pan or line it with parchment paper.

Peel, core, and dice the apples into small, even pieces. Blot away excess moisture if needed.

In a large bowl, whisk together the melted butter and brown sugar until combined.

Allow the butter mixture to cool slightly. Add the egg and vanilla extract, then whisk until smooth.

In a separate bowl, combine the flour, cinnamon, baking powder, and salt.

Add the dry ingredients to the wet ingredients and stir gently until no dry flour remains.

Fold in the diced apples and optional chopped walnuts or pecans.

Spread the thick batter evenly in the prepared baking pan.

Bake for 25–35 minutes, until the edges turn golden and the center looks set. A toothpick should come out with a few moist crumbs.

Place the pan on a cooling rack and allow the bars to cool completely.

Lift the bars from the pan using the parchment paper, if used, and cut into 12–16 squares.

Dust with powdered sugar if desired, and serve plain or with vanilla ice cream.