Preheat oven to 350°F (175°C). Line a 9"x 13" pan with parchment paper so that the paper overhangs by a couple of inches on the two long sides. Grease the paper. (The parchment makes things simpler, but you can also skip that step and just grease the pan if you prefer.)
Whisk together the flour, baking powder, and salt. Set aside.
Combine the cooled butter, brown sugar, and sugar using a large spoon or an electric mixer on medium-low speed.
Add the eggs, one at a time, mixing well after each addition. Mix in the vanilla.
Gradually add the flour mixture, mixing just until a few streaks of flour remain.
Stir in the remaining ingredients, mixing just until combined.
Transfer the dough to the prepared pan, and spread evenly.
Bake 30 to 35 minutes, or until the edges are brown and a pick inserted into the center comes out clean.
Cool in the pan on a wire rack. Then use the overhanging parchment paper to lift the bars out of the pan and onto a cutting board. Cut into bars.
Notes
Use any combination of add-ins that you like. Just keep the total amount around 2 & 1/2 cups.