For cookies: In a very large mixing bowl, beat the butter with an electric mixer on medium to high speed for 30 seconds. Gradually add powdered sugar. Beat until the mixture is combined, scraping sides of bowl occasionally. Add vanilla. Add eggs, one at a time, beating 1 minute after each addition. Beat in the flour. (Dough will be sticky.) Cover and chill dough 6 to 24 hour or until easy to handle.

Line cookie sheets with parchment paper, nonstick foil or a silicone baking mat (Silpat). Shape dough into 1-inch balls. Place balls 2 inches apart on prepared cookie sheets. Dip the bottom of a damp glass in granulated sugar and use to flatten each ball to a 2-inch circle. Bake in a 350 degree F oven about 12 minutes or until edges are just beginning to brown. Transfer cookies to wire racks; cool.

Spread bottoms of half the cookies with jam. Top with remaining cookies, bottom sides down. Set aside.

For chocolate dip: Place chocolate pieces and shortening in a heavy small saucepan. Heat over low heat, stirring frequently until melted. (If the mixture becomes too thick during dipping, reheat in the saucepan. Stir the mixture constantly until it once again reaches dipping consistency.)

For the vanilla dip: Coarsely chop the vanilla-flavored candy coating. Place in another heavy small saucepan. Heat over low heat, stirring frequently until melted. If needed, reheat the candy coating as above.

Dip half of the sandwich cookies halfway in the melted semisweet chocolate pieces, and the remaining cookies in the melted vanilla-flavored candy coating. Allow excess chocolate or coating to drip off cookie. Place dipped cookies on a baking sheet lined with waxed paper. If you like, drizzle the cookies with additional coating of a different color. Let the dipped cookies stand at room temperature, uncovered, on the waxed paper until set. Makes 4 dozen sandwich cookies.