Place the butter into a medium saucepan over medium heat. Let the butter cook while occasionally stirring to ensure the butter is cooking evenly.
Cook the butter until it is a deep golden brown color and smells nutty and toasted, about 5 -7 minutes. Remove the pan from the heat.
Let the butter cool to room temperature. Place the butter in the refrigerator until solid but scoopable.
Combine the butter, the confectioner's sugar and the salt into a bowl of a stand mixer.
Beat on low speed until combined, stopping to scraping the bowl to ensure all ingredients are well mixed.
Add the flour and the pecans to the butter mixture and mix until just combined, and no flour remains in the bowl.
Transfer the dough to a lightly floured surface or a non-stick mat, and form the dough into a ball. Flatten to a disc, about 1" high, and wrap tightly with plastic wrap.
Chill the dough in the refrigerator for 30 minutes.
Roll and cut out the cookies:
Heat the oven to 350F. Line two cookies sheets with parchment.
On a lightly floured surface or a non-stick mat, roll out the dough to about 1/4" thick.
Using a round fluted cookie cutter, cut out rounds out of the dough and place on the parchment cookie sheets, leaving about 2" between the cookies.
Bake the cookies for 17-20 minutes until the edges are just starting to lightly brown. Cool for 10 minutes on the cookie sheets. Transfer the cookies to a cooling rack to cool completely.
Make the maple glaze:
In a medium bowl, whisk together the confectioner's sugar, salt, maple syrup, water, and maple extract until smooth.
Dip half of the cookies into the glaze and place on parchment paper.
While the glaze is still wet, sprinkle with finely chopped pecans.
Let the glaze set completely before serving.
Notes
Cookies will stay fresh in an airtight container for up to a week.