Lightly spoon flour into dry measuring cups; level with a knife. Combine flour, pecans, and salt, stirring well with a whisk.
Place granulated sugar and butter in a medium bowl; beat with a mixer at medium speed until fluffy (about 2 minutes). Beat in vanilla extract. Beating at low speed, gradually add flour mixture, and beat just until combined (mixture will be crumbly).
Shape dough into 34 (1-inch) balls (about 1 tablespoon each). Place dough balls 2 inches apart on baking sheets coated with cooking spray. Bake at 350° for 20 minutes or until lightly browned.
While cookies are still hot, sift powdered sugar evenly over 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.