1cup2 sticks unsalted butter, cut into 1-inch cubes
1 ½cupsall-purpose flour
1/2teaspoonbaking soda
1/4teaspoonbaking powder
1cupdark brown sugar
1/4teaspoonsalt
1egg
1teaspoonvanilla
1/2cuptoasted pecans, chopped and divided
For the Frosting:
1/4cupreserved brown butter
1teaspoonsvanilla
1 ½cupspowdered sugar
2tablespoonsmilk
Instructions
Adjust oven rack to middle position and heat oven to 350 degrees F. Line 2 baking sheets with parchment paper.
In 10-inch skillet over medium-high heat, heat butter until melted, about 2 minutes. Continue to cook, stirring constantly until butter is dark golden brown and has nutty aroma, 1 to 3 minutes. Remove skillet from heat and transfer browned butter to the heat-proof bowl of a stand mixer (Reserve ¼ cup of browned butter for frosting); set aside to cool for 15 minutes. In medium bowl, whisk together flour, baking soda, and baking powder; set aside.
Add brown sugar and salt to bowl with cooled browned butter; attach paddle and mix on medium-low speed until no sugar lumps remain, about 30 seconds. Scrape down sides of bowl with rubber spatula; add egg, and vanilla and mix on medium-low speed until fully incorporated, about 30 seconds. Scrape down bowl. Add flour mixture and mix until just combined, about 1 minute. Fold in 1/3 cup chopped pecans.
Drop by rounded tablespoons onto prepared baking sheets, spacing 2 inches apart. Bake for 10-12 minutes. Transfer the baking sheet to a wire rack and let the cookies cool on the sheet for 2 minutes then using a wide metal spatula, transfer the cookies to the rack to cool completely.
To make the frosting, beat reserved browned butter, vanilla, powdered sugar, and milk in the bowl of a stand mixer fitted with the paddle attachment until thoroughly combined. If frosting is very thick add a splash of milk until correct consistency. Spread over cooled cookies and sprinkle remaining chopped pecans.