Preheat oven to 325°.
In a large bowl, cream butter and confectioners' sugar until light and fluffy.
Beat in vanilla. Gradually add flour to creamed mixture and mix well.
Stir in pecans. Roll into 1-in. balls. Place 1 in. apart on ungreased baking sheets. Using the end of a wooden spoon handle, make an indentation in the center of each.
Bake 18-20 minutes or until lightly browned.
Roll warm cookies in additional confectioners' sugar; cool on wire racks.In a microwave, melt chocolate chips; stir until smooth. Stir in corn syrup, water and shortening. Spoon or pipe into cooled cookies.