Brown the butter: Melt butter in a saucepan over medium heat. Once it starts bubbling, constantly whisk so it doesn’t burn. Cook until butter is brown and has a nutty smell to it. Transfer to a bowl and cool in the fridge until it’s reached the consistency of softened butter.
In the bowl of a stand mixer with a paddle attachment, cream together butter and sugar until light and fluffy. Add vanilla extract and salt; beat until combined. Add flour and beat until incorporated. Gently fold in pecans.
Roll or scoop dough into 1-inch balls. Refrigerate for 30 minutes. Preheat oven to 350 degrees.
Bake on a cookie sheet, each cookie about 1 to 2 inches apart, for 10 to 12 minutes, until the cookies are just beginning to set and about to brown. Let cookies cool slightly, roll them in powdered sugar. Let cookies cool completely and roll in powdered sugar once more.