Preheat the oven to 350°F. Line baking sheets with parchment paper or silicone mats.
In a medium bowl, whisk together the flour, pecans, and salt.
In a separate medium bowl, combine the granulated sugar and butter with an electric mixer at medium speed until fluffy (about 2 minutes). Beat in the vanilla extract. Beating at low speed, gradually add the flour mixture, and beat just until combined (mixture will be crumbly). You should be able to form the dough into balls. If the mixture is too crumbly, go ahead and add several drops of milk or water until the mixture comes together more easily.
Shape the dough into 34 (1-inch) balls (about 1 tablespoon each). Place the dough balls 2-inches apart on the prepared baking sheets. Bake for 20 minutes or until lightly browned.
While the cookies are still hot, sift powdered sugar evenly over the tops. Remove from pan; cool completely on wire racks.
It is important for your butter to be soft when you prepare the dough so it will hold together nicely when you shape it into balls.