Heat oven to 350°F (175°C). Line a 9-by-13-inch metal pan with parchment, leaving overhang on two sides.
Melt butter in a light-colored saucepan over medium heat, stirring often. Continue cooking 5 to 8 minutes until the milk solids turn amber and smell nutty. Immediately pour into a heatproof bowl, scraping in the browned bits. Stir in 2 tablespoons water and cool 10 minutes.
Whisk brown sugar and granulated sugar into the warm butter until no dry pockets remain. Whisk in eggs one at a time, then vanilla.
In a separate bowl, whisk flour, baking powder, and salt. Fold into the butter mixture just until no dry flour remains; fold in pecans. Do not overmix.
Spread batter evenly in the prepared pan. Bake 24 to 29 minutes, until edges are set and lightly golden and the center is just set but still soft. A toothpick should show moist crumbs, not wet batter. Avoid waiting for a completely clean toothpick.
Cool completely in the pan, about 90 minutes, before lifting out and cutting into 16 bars. The center firms as it cools.