In the bowl of a stand mixer with the paddle attachment, cream the butter until soft. Add brown sugar and process for 2 minutes.
Meantime, in a mixing bowl, combine flour with salt; whisk until well blended.
Add ½ flour mixture to the butter mixture and process on low speed until somewhat mixed. Add the remaining flour and process again until well incorporated. While processing, add vanilla extract.
Add chopped pecans and process until the nuts are evenly distributed, about 1 minute.
Transfer the dough to a bowl, cover with plastic wrap, making sure it touches the surface, and chill for 1 hour.
Preheat oven to 350ºF.
Form 12 little balls and place them on a cookie sheet. Using the bottom of a measuring cup or a glass, dip in granulated sugar before flatten the balls. Place one half pecan per cookie pressing down gently.
Transfer to the preheated oven and bake for 15 minutes, rotating the cookie sheet halfway thru cooking.
Remove from the heat and let the cookies cool off on the sheet for 10 minutes before transferring them to a wire rack to cool completely.