Preheat oven to 350 degrees F (175 degrees C). Grease cookie sheets.
Step 2
In a medium bowl, cream together the butter and confectioners' sugar until light and fluffy. Stir in the vanilla and then the flour to form a soft dough. Roll the dough into walnut sized balls. Place the cookies 2 inches apart onto the cookie sheet. Flatten each cookie to 1/4 inch thick using the bottom of a glass dipped in confectioners' sugar.
Step 3
Bake for 8 to 10 minutes in the preheated oven, until the edges are just beginning to brown. Do not over cook. Remove from cookie sheets to cool on wire racks.
Step 4
Melt the coating chocolate over a double boiler or in the microwave, stirring frequently until smooth. Spread chocolate onto the bottom of each cookie. Place cookies chocolate side down onto waxed paper until set.