1. Preheat your oven to 350°F (175°C) and line an 8×8 inch baking pan with parchment paper.
2. In a medium bowl, whisk together the flour, baking powder, and salt. Set aside.
3. In a large bowl, combine the melted butter and brown sugar, stirring until smooth and well-blended.
4. Add the egg and vanilla extract to the butter mixture, mixing until fully incorporated.
5. Gradually add the dry ingredients to the wet ingredients, stirring just until combined.
6. Fold in the chocolate chips and walnuts, ensuring they are evenly distributed throughout the batter.
7. Pour the batter into the prepared pan and smooth the top with a spatula.
8. Bake for 25-30 minutes, or until the edges are golden brown and a toothpick inserted into the center comes out clean.
9. Allow the bars to cool in the pan for 10 minutes before transferring them to a wire rack to cool completely.

Remember, patience is key here. Allowing the bars to cool will help them set properly, making them easier to cut and enjoy.