Preheat oven to 350Â°.
In a small bowl, cream butter and sugar until light and fluffy. Beat in egg. In another bowl, whisk flour, cocoa, salt and baking soda; gradually beat into creamed mixture.
Shape dough into 1-inch balls (small cookie scoop works well); place 2 inches apart on ungreased baking sheets. Flatten to 2-inch rounds with the bottom of a glass. Bake 6-8 minutes or until set (do not overbake). Cool on pans 5 minutes. Remove to wire racks to cool completely.
In a microwave, melt white chocolate with 1 teaspoon oil; stir until smooth. Drizzle over cookies. Repeat with semisweet chocolate and remaining oil. Sprinkle tops with crushed candy canes; let stand until set.