Melt butter in a light-colored saucepan over medium heat, swirling occasionally. Continue cooking 3-5 minutes until the butter foams, then subsides, and golden-brown bits form on the bottom. The smell will turn intensely nutty and caramel-like. Immediately pour into a heatproof bowl, scraping in all the brown bits. Let cool 10-15 minutes until lukewarm but still liquid.

In a medium bowl, whisk together flour, baking soda, and kosher salt. Set aside.

In a large bowl, whisk together brown sugar, granulated sugar, and the cooled brown butter until well combined and glossy, about 1 minute. The mixture will look like wet sand.

Whisk in eggs one at a time until fully incorporated, then whisk in vanilla. The dough should look smooth and slightly thickened.

Switch to a rubber spatula and fold in the flour mixture until just combined with a few streaks remaining. Add the toasted pecans and fold until no dry flour remains. Do not overmix.

Cover and refrigerate dough 20-30 minutes while you preheat the oven to 350°F. This firms up the brown butter and prevents spreading.

Line baking sheets with parchment. Scoop 2-tablespoon portions of dough, spacing 2 inches apart. Bake 11-13 minutes until edges are set and golden but centers still look slightly underdone. Rotate pans halfway through.

Let cookies cool on pans 5 minutes to finish setting, then transfer to wire racks. Sprinkle with flaky sea salt while warm if desired. Cool completely before storing.