Preheat the oven and toast the pecans: Arrange an oven rack in the center position and preheat the oven to 3500 F. Scatter the pecans on a small rimmed baking sheet and toast, tossing halfway through, until they're golden and nutty smelling, 8 to 10 minutes. Remove the baking sheet from the oven and set aside to allow the pecans cool.

Make the brittle: Meanwhile, line a small rimmed baking sheet with parchment paper and set aside. In a small saucepan, combine the granulated sugar, butter, and 2 tablespoons of water (1 oz / 2 8g) and cook over medium- low heat, stirring gently with a heatproof spatula to dissolve the sugar. Increase the heat to medium and bring the syrup to a rapid simmer. Cook without stirring, swirling the pan often, until the syrup turns a deep amber color, 8 to 10 minutes. Immediately remove the saucepan from the heat and stir in the pecans. Once the pecans are well coated, add the baking soda and salt and stir quickly to incorporate—the mixture will rapidly foam and sputter as the baking soda aerates the caramel. Quickly scrape the brittle out onto the prepared baking sheet and spread into a thin layer, if possible, before it starts to harden (which happens very quickly). Set the baking sheet aside until the brittle is completely cooled, 5 to 10 minutes. Chop the brittle into pea-sized bits and set aside.

Brown the butter: Measure out 4 ounces (113 g) of the butter, place in the bowl of a stand mixer, and set aside. Place the other 4 ounces (113 g) butter in a small saucepan and cook over medium-low heat, stirring frequently, until the butter comes to a boil. Continue to cook, scraping the bottom and sides of the pan constantly with a heatproof spatula, until the butter sputters, foams, and eventually you see browned bits floating about, 5 to 7 minutes. Add the browned butter to the stand mixer bowl, making sure you scrape in all the browned bits. Set the bowl aside to cool until the butter begins to resolidify, about 30 minutes.

Blitz the dry ingredients: In a food processor, combine the flour, salt, and baking soda, then add half of the pecan brittle bits and 1 cup (3.5 oz / 100g) of the oats. Blitz the mixture in long pulses until the oats and brittle are broken down and finely ground. Set aside.

Mix the batter: Set the bowl of cooled butter on the mixer and attach the paddle. Add the dark brown and granulated sugars and beat on medium speed until the mixture is light and smooth but not fluffy, about 2 minutes. Scrape down the sides of the bowl, add the eggs and vanilla, and continue to beat until you have a very light and satiny mixture, about 1 minute. Scrape down the sides of the bowl and add the flour/oat/brittle mixture and beat on low until no dry spots remain and you have a soft, evenly mixed dough. Add the remaining pecan brittle bits and 1 cup (3.5 oz / 100g) oats and mix on low again just until dispersed. Fold the batter several times with a flexible spatula to ensure everything is evenly mixed.

Scoop and chill the batter: Using a 2-ounce scoop or ¼-cup measure, scoop level portions of dough and place on a parchment-lined baking sheet as close together as possible (you'll space them out before baking). Cover the dough tightly with plastic wrap and refrigerate for at least 12 hours and up to 48. (If you're pressed for time, a couple of hours in the refrigerator will do. Just note the baked cookies won't be as chewy.)

Preheat the oven and prepare the pans: When you're ready to bake, arrange two oven racks in the upper and lower thirds of the oven and preheat to 350 F. Line two large rimmed baking sheets with parchment paper.

Bake the first batch of cookies: Place 6 pieces of chilled cookie dough on each of the prepared baking sheets, spacing so they're at least 3 inches apart. Bake the cookies on the upper and lower racks until they are dark golden brown around the edges, 16 to 20 minutes, switching racks and rotating the sheets front to back after 12 minutes. Allow the cookies to rest for 5 minutes on the baking sheets, then use a metal spatula to transfer the cookies to a wire rack to cool.

Bake the remaining cookies: Carefully move one of the oven racks to the center position, place the remaining dough on one of the baking sheets (it's okay if it's still warm), and bake on the center rack (this last sheet might bake a bit faster than the first two).