Preparation

• Using the 8 oz. of butter, prepare the brown butter as directed in the masterBrown Butterrecipe. Refrigerate the butter until firm, 30 minutes to one hour.
• In a medium skillet over medium heat, melt the remaining 1 Tbs. butter. When it starts to bubble, add the pecans and stir constantly until the nuts are warmed through and smell toasty, 2 to 3 minutes. Scrape the nuts onto a baking sheet, and sprinkle with 1 Tbs. of the sugar. Toss to coat, then cool completely. When cool, coarsely chop 1 cup of the nuts and set aside. Finely chop the remaining nuts.
• In the bowl of a stand mixer fitted with the paddle attachment, beat the cold brown butter on medium speed until creamy, about 1 minute. Add the remaining 3/4 cup sugar, and beat well. Add the egg yolk and vanilla, and beat to combine well, stopping to scrape down the bowl with a silicone spatula. Add the flour and salt, and mix on low speed until the dough is soft and smooth. Using a silicone spatula, stir in the coarsely chopped pecans, and then gently work them into the dough by hand.
• Scrape the dough onto a lightly floured work surface, and divide into two pieces. Roll each piece into a log about 6 inches long and 1-1/2 inches thick. Wrap each log in parchment, twisting the ends tightly. Refrigerate until firm enough to slice, 2 hours or up to overnight.
• Remove one dough log from the refrigerator, unwrap it, and brush generously with half of the reserved egg white. Roll the log in half of the finely chopped pecans, making sure that the log is completely covered with nuts, pressing them into the dough with your hands, if necessary. Using a sharp knife, slice the log into rounds slightly less than 1/2 inch thick. Repeat with the remaining dough log.
• Position a rack in the center of the oven, and heat the oven to 300°F. Line a large rimmed baking sheet with parchment. Place the slices on the baking sheet, 1 inch apart. Bake for 18 to 21 minutes, until the shortbread loses its shine and feels set and slightly firm to the touch. The cookies should not brown. Transfer the baking sheet to a wire rack, and allow the cookies to cool on the pan. When the shortbread is completely cool, transfer to a serving plate, or store in a tightly covered container for up to one week.