Preheat oven to 350 degrees.
Lightly grease 2 baking sheets. In the bowl of a mixer, combine the butter and vanilla. Add 1/2 cup of the sugar, then slowly add the flour and pecans and mix just until combined. Use your hands to roll the dough into balls about 3/4-inch in diameter, and arrange them on the baking sheets. Bake 15 to 20 minutes, until golden brown. Meanwhile, spread the remaining confectioners' sugar out on a plate. When the cookies are done, remove from the oven, let cool 3 to 5 minutes, and then roll each cookie in the sugar until coated, letting each rest in the sugar for a minute to absorb it. Let cool completely on wire racks, then store in airtight containers.
Recipe courtesy of Gale Gand, "American Brasserie" by Gale Gand, Rick Tramonto, Julia Moskin, MacMillian, Publishers, 1997