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In a food processor, combine the brown butter, pecans, powdered sugar, vanilla extract, and salt and pulse until a thick paste forms, scraping down the bowl of the food processor a few times during the pulsing. Remove the filling from the food processor, cover, and chill while you are making the cookie dough.
To make the cookie dough, sift the flour, cocoa, and baking soda together into a bowl. Set the dry ingredients aside.
In the bowl of an electric mixer with the paddle attachment, combine the butter and sugar and cream together on medium-high speed until very pale and fluffy, about 3 minutes. Scrape down the bowl.
Add the egg on medium-low speed and beat to incorporate.
Scrape the bowl and the paddle and add the pecans, vanilla extract, and salt.
Add the dry ingredients on low speed in 3 or 4 additions and mix until just combined. Do not overmix. Remove the bowl from the mixer and scrape down all the way to the bottom of the bowl with a rubber spatula, to be sure everything is well mixed.
Chill the cookie dough an hour or longer before shaping.
When you are ready to shape and bake the cookies, preheat the oven to 375degreesF. Portion the dough using a 1/3-ounce (or #100) ice cream scoop. (If you dont have a scoop, use about 2 teaspoons of dough per cookie.) You should get 48 cookies.
Place the cookies 3/4 to 1-inch apart on parchment-lined baking sheets and use your fingers to press them flat, a little less than 1/4-inch thick. (You should be able to get 16 cookies on each baking sheet and bake in 3 batches). Bake until cooked through and the cookies feel set, about 7 minutes. Do not open the oven door while they are baking. Remove the pan from the oven and allow to cool at least 10 minutes before removing the cookies with a metal spatula. Cool cookies completely before filling.
To make a cookie sandwich, turn one cookie flat side up and spread with about 2 teaspoons of filling (you can use the same small ice cream scoop that you used for the cookie dough to portion out the filling), then top with another cookie flat side down, pressing gently. Repeat until all the cookies are sandwiched together.