Cream shortening; gradually add sugar, beating until light and fluffy. Add egg; beat well.
Combine flour and salt; add to creamed mixture, beating well. Stir in vanilla.
Drop batter by teaspoonfuls onto greased baking sheets. Press a pecan half in center of each cookie. Bake at 325° for 10 minutes or until lightly browned. Cool slightly on baking sheets; remove to wire racks, and let cool completely.