Heat oven to 350°F. Line two baking sheets with parchment paper.
Beat the butter and 1/2 cup of the powdered sugar with an electric mixer until light and creamy, about 2 minutes; beat in the vanilla.
Add the flour and salt and mix on low just until the dough comes together, then stir in the pecans. If it looks crumbly, press it together by hand.
Roll the dough into 1-inch balls (about 36) and place 1 inch apart on the sheets.
Bake both sheets at once for 14-16 minutes, rotating top to bottom halfway through, until set with barely golden bottoms. Cool on the sheets 10 minutes.
Roll the warm cookies in the remaining 1 cup powdered sugar, cool completely on a rack, then roll once more in sugar.