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