Preheat the oven to 350F.
In a large bowl, beat the butter, icing sugar and vanilla for 2-3 minutes, until pale and light. Add the flour and salt and stir or beat on low until the dough starts together; add the pecans as you stir.
Roll the dough into walnut-sized balls and place on an ungreased or parchment-lined baking sheet. Bake for 12-15 minutes, until very pale golden. Place some icing sugar in a shallow bowl and roll the cookies in the icing sugar to coat almost as soon as they come out of the oven - while they’re still very warm. The butter will seep into the icing sugar, giving them an icing-like coating; if you like, roll them in icing sugar a second time, after they’ve cooled slightly.
Makes 2 dozen cookies.