• Make brown butter. First brown the butter. Follow the instructions in this post here to learn how to brown butter. It’s easy! Brown specks and a dense golden foam will form at the surface when it is nearly ready. Pour it out into a clean bowl and let it cool for 10 minutes. This whole process takes around 8-10 minutes. Immediately pour it into a large mixing bowl, then let it cool for 20-30 minutes until it reaches a temperature just warmer than room temperature. If you care to measure, the butter should read 34°C or 93°F on a thermometer.
• Combine cooled (but still liquid) brown butter with both sugars in a large bowl and beat with an electric hand mixer or using a whisk until smooth, pale, slightly fluffy and creamy-looking. Beat in egg and vanilla until well incorporated.
• Combine flour, baking soda and salt in a medium bowl and whisk to blend evenly. Add it to the butter mixture. Mix gently until incorporated and then fold in chopped pecans with a spatula. Use your hands to bring the dough together and incorporate the pecans evenly since the dough will be stiff. Place it onto a large piece of plastic wrap or parchment paper and roll it into a thick 9 to 10-inch log. Wrap well and refrigerate for about 1 hour or until firm.
• Preheat oven to 350°F. Line two large cookie sheets with parchment paper.
• Use a sharp knife to slice the chilled cookie dough log into rounds with just about ½-inch thickness and place them onto prepared baking sheets spacing them about 2 inches apart. If the dough is too hard, let it rest at room temperature for 10 minutes before slicing.
• Bake for 10-12 minutes until golden brown. Transfer baking sheets to a wire rack to cool completely, then dip and drizzle with melted white chocolate if desired. Let chocolate set before storing in an airtight container.

NOTE: Since brown butter has all of its water removed, it essentially becomes pure milk fat and it is no longer an emulsion. As a result, the cookies will feel slightly greasy when warm but will handle just fine once cooled.