Preheat your oven to 350°F (175°C). Line an 8×8-inch square baking pan with parchment paper, leaving an overhang on the sides to easily lift the blondies out later. Grease the paper slightly with cooking spray.
Place the butter in a medium saucepan over medium heat. Melt the butter, then continue cooking it while stirring constantly. The butter will foam, then clear, and eventually turn a golden brown color with dark bits at the bottom. Once it smells nutty and looks like amber, remove it from the heat immediately so it does not burn.
Pour the hot brown butter into a large mixing bowl. Add the brown sugar and whisk until well combined and smooth. Let the mixture cool for about 5 minutes before whisking in the eggs one at a time, followed by the vanilla extract.
Using a spatula, gently fold in the flour, baking powder, and sea salt. Stir only until no streaks of flour remain. Be careful not to overmix, as this can make the blondies tough rather than chewy.
Fold in the toasted chopped pecans. The batter will be quite thick and glossy at this stage.
Spread the batter evenly into your prepared baking pan. Bake for 22 to 25 minutes. The edges should be set and slightly pulled away from the sides, while the center should still look a little soft. A toothpick inserted into the center should come out with a few moist crumbs.
Place the pan on a wire rack and allow the blondies to cool completely in the pan. This is crucial for the texture to set. Once cool, lift them out using the parchment paper and cut into 16 squares.