Cream butter in a large mixing bowl; gradually add sugar, beating well. Add egg, and beat well. Stir in vanilla.
Dissolve soda in buttermilk; add to creamed mixture, stirring well. Gradually add flour; mix well. Chill 1 hour.
Divide dough in half, keeping one half chilled until ready to use. Roll to 1/4-inch thickness on a well-floured surface, and cut with a floured 2 1/2-inch round cutter.
Place 1 inch apart on lightly greased cookie sheets. Bake at 350° for 8 to 10 minutes. Remove from cookie sheets, and cool on wire racks. Repeat procedure with remaining dough.