Preheat the oven to 350 degrees F. Line an 8-inch square pan with parchment paper, leaving a 2-inch overhang on 2 sides.
In a medium saucepan, heat the butter over medium-high heat until melted. Continue to cook the butter, swirling the pan often, until the milk solids turn golden brown and the butter smells nutty, about 5 minutes.
Remove the pan from the heat and let it cool for a few minutes. (You don't want the egg to scramble when you stir it in.) Stir in the brown sugar until smooth. Then stir in the egg and the vanilla extract. Stir in the flour, salt, baking powder, and baking soda. Then add half of the chocolate and half of the macadamia nuts. The batter will be thick.
Tip the mixture out into the prepared pan. Use an offset spatula to smooth the dough to an even thickness. Sprinkle with the remaining chocolate and macadamia nuts. Bake until the dough is puffed and a toothpick inserted into the center comes out with moist crumbs attached, 20 to 25 minutes. Let cool on a rack. Using the parchment, lift the bar out of the pan and onto a cutting board. Cut into pieces and serve.