Optional: toast the pecans! Heat the oven to 300°F and spread pecans on a baking sheet. Toast for 5 minutes, until they just begin to color and you can smell them baking. Let them cool completely before chopping and adding to the dough.
Beat the butter for two minutes, until light and fluffy. Add 3/4 cups powdered sugar and beat another minute until creamed.
Add the vanilla and combine.
In a separate bowl, combine the flour and salt. Add half the mixture to the butter and stir on low until just combined. Then add the other half and the chopped pecans and stir again until just combined.
Wrap the dough in wax paper and refrigerate for at least 45 minutes.
When ready to bake, preheat the oven to 350°F. Roll the dough into balls, being gentle with the dough - try to not overhandle it.
Bake on an ungreased baking tray for 9-11 minutes. They won't spread, so it's okay to put them closer together. While they bake, put the remaining powdered sugar in a bowl and set aside.
Transfer to a cooling rack. As soon as they're cool enough to touch (but still warm), toss the cookies in the bowl of powdered sugar and coat.