To prepare cookies, lightly spoon flour into a dry measuring cup; level with a knife. Combine flour, baking soda, and salt in a bowl, stirring well with a whisk; set aside. Beat butter with a mixer at medium speed until light and fluffy. Gradually add granulated sugar, beating until well-blended. Add vanilla and egg white; beat well. Add flour mixture; stir until well-blended. Turn dough out onto wax paper; shape into a 6-inch log. Wrap log in wax paper; freeze for 3 hours or until very firm.
Preheat oven to 350°.
Cut log into 24 (1/4-inch) slices; place the slices 1 inch apart on a baking sheet coated with cooking spray. Bake at 350° for 8 to 10 minutes. Remove the cookies from pan, and cool on wire racks.
To prepare the icing, combine powdered sugar and cocoa in a small bowl; stir well. Add milk; stir well. Spread over cookies to within 1/4 inch of edges. Place semisweet and white chocolate in separate heavy-duty zip-top plastic bags; seal. Microwave chocolates at high for 1 minute or until chocolates are soft. Knead the bags until smooth. Snip a tiny hole in corner of bags; drizzle chocolates over the frosted cookies so that they resemble truffles.