Preheat the oven to 350°F. Spread the chopped pecans on a baking sheet and toast for 7–9 minutes, stirring halfway through, until fragrant and lightly darkened. Let cool.
Melt the butter in a saucepan over medium heat. Cook, stirring frequently, until the milk solids turn golden brown and smell nutty, about 5–8 minutes. Immediately pour into a large heatproof mixing bowl, scraping in the browned bits.
Let the browned butter cool for about 20 minutes, until lukewarm. Stir in the water. For the most consistent results, weigh the browned butter and add enough water to bring the combined weight back to 226 g. Do not add the water while the butter is hot.
Whisk the light brown sugar and granulated sugar into the cooled butter. Add the egg, egg yolk, and vanilla, then whisk until smooth and combined.
In a separate bowl, whisk together the flour, baking soda, and fine salt. Fold into the wet mixture just until no dry flour remains. Fold in the cooled pecans. If desired, reserve a few pieces from the measured pecans for the tops.
Cover and refrigerate for at least 1 hour or overnight. If chilled overnight, let the dough sit at room temperature for about 15–20 minutes, until scoopable.
Preheat or return the oven to 350°F. Line baking sheets with parchment paper. Scoop approximately 2-tablespoon portions of dough, spacing them about 3 inches apart. Slightly flatten the tops. Press any reserved pecans onto the portions.
Bake one sheet at a time on the middle rack for 11–13 minutes, until the edges are golden and set but the centers still look slightly soft. Keep remaining dough chilled between batches and use a cool baking sheet for each batch.
Sprinkle with optional flaky salt. Let the cookies rest on the baking sheet for 10 minutes, then transfer to a wire rack to cool completely.