Stuff each date with a pecan half, and set aside.
Cream butter in a medium mixing bowl; gradually add sugar, beating well. Add egg; beat well.
Sift together flour, baking powder, soda, and salt; add to creamed mixture alternately with sour cream, beginning and ending with flour mixture. Fold in prepared dates.
Drop dough by heaping teaspoonfuls 2 inches apart onto greased cookie sheets, allowing 1 date per cookie. Bake at 375° for 6 minutes or until lightly browned. Remove from cookie sheets, and cool on wire racks.