1. Heat oven to 350F. Beat butter and sugar in large bowl with electric mixer until fluffy. Beat in remaining ingredients, except flour and crystallized ginger, until blended (mixture will look curdled).
2. With mixer on low speed, add flour and beat just until blended; stir in crystallized ginger.
3. Drop by level tablespoonfuls 2 in. apart on ungreased baking sheets. Bake 10 to 12 minutes until tops look dry. Cool on baking sheet 1 minute before removing to wire rack to cool completely.
4. Spread a rounded teaspoon buttercream frosting on each cooled cookie. Sprinkle with slivered crystallized ginger. Refrigerate in an airtight container with wax paper between layers.
Buttercream Frosting:
Beat ingredients in medium bowl with electric mixer until smooth. Then beat on high speed 1 minute until fluffy.
Mint Use 1⁄4 tsp peppermint extract instead of vanilla; add a few drops of green food color.
Coffee Dissolve 1 Tbsp instant coffee in 1 Tbsp hot water; add instead of milk.
Apple Instead of milk, add 1 to 2 Tbsp apple juice until spreadable