In a medium sauce pan over medium low heat, 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.
1 cup unsalted butter
Let the butter cool to luke warm, for about an hour. Place the cooled butter in the refrigerator until solid but scoopable and still soft, for an additional 1-2 hours. The texture will be similar to shortening, or tub butter.
In the bowl of a stand mixer fitted with the paddle attachment, beat together the brown butter, confectioners' sugar and the salt until well combined.
½ cup confectioners sugar, ½ teaspoon fine sea salt
Beat in the flour and the pecans until just combined, and no large pockets of flour remains in the bowl. If the dough is still dry and sandy, stream in the cream until the dough starts to come together.
2 cups all purpose flour, ½ cup pecans, toasted and finely chopped (plus some for sprinkling), 2-3 tablespoons cream or half and half
Transfer the dough to a lightly floured surface or a non-stick mat, and form the dough into a ball. Wrap tightly with plastic wrap and flatten to a disc, about 1" high. Chill the dough in the refrigerator for 30 minutes.
Preheat 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 ¼" 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. Chill the cookies for 20 minutes.
Bake the cookies for 15-17 minutes until the edges are just starting to lightly brown and the centers of the cookies look set. Cool the cookies completely on the baking sheet.
In a medium bowl, whisk together the confectioner's sugar, maple syrup, and maple extract until smooth. Add the water as needed. The glaze consistency should be thick enough to coat the cookie, similar to melted chocolate in texture.
2 cups confectioners sugar, 3 tablespoons maple syrup, 2-3 tablespoons water, ½ teaspoon maple extract, ⅛ teaspoon fine sea salt
Dip the cookies into the glaze, halfway, then place on parchment paper.
While the glaze is still wet, sprinkle with finely chopped pecans. Let the glaze set before serving or storing.