Preheat oven to 325 degrees. Break each pecan
half into 2 or 3 pieces. Cream butter and sugar with a mixer until pale. With mixer running, add vanilla and salt, then reduce speed to low. Gradually add flour, beating until just incorporated. Stir in pecans until distributed evenly. Cover dough, and refrigerate until firm, 15 minutes
(or overnight; let dough come to room temperature before using).
Drop 2-tablespoon scoops of dough onto baking sheets, 2 inches apart. Bake, rotating sheets halfway through, until edges of cookies are golden, about 15 minutes. Let cool on sheets on wire racks for 5 minutes. Transfer cookies to wire racks, and let cool. Dust with confectioners' sugar just before serving.
Cookies will keep, covered, for up to 2 days.