Preheat over to 350.
On a baking sheet, toast pecans about 6 minutes, or until fragrant. Let cool, finely chop.
With an electric mixer, cream butter and 1/3 cup sugar until light, about 1 minute.
Beat in salt, vanilla, and flour, scraping down sides of bowl, just until dough comes together. Fold in pecans.
Separate dough into 12 pieces; squeeze down to shape into balls.
Roll in sugar. Place 3 inches apart, on a baking sheet topped with parchment paper. Gently flatten with the bottom of a glass (reshape sides if necessary).
Sprinkle with sugar.
Bake until golden brown, rotating halfway through, about 15 minutes.
Cool cookies on a wire tack.