Combine 2 1/2 cups (610 mL) flour, baking soda, and salt in medium bowl; set aside.
Mix in eggs and vanilla extract until blended.
Gradually add in flour mixture; mix just until blended. Stir in additional 1/4 cup (60 mL) flour and peppermint extract.
Divide dough in half (about 1 2/3 cups). Stir cocoa powder into half and candies into the other half. Roll out cream dough between 2 sheets of parchment or wax paper into 10 x 16 inch rectangle. Repeat with cocoa dough.
Using parchment paper, place cream dough on top of cocoa dough, trimming excess so dough is even. Gently roll dough lengthwise into log, using the parchment paper to assist (dough will be soft). Make sure to not leave in any paper.
Carefully roll log into peppermint candies, using parchment paper to assist. Wrap log in parchment paper then plastic wrap. Place on cookie sheet and freeze 24 hours.
Preheat oven to 375°F (190°C). Unwrap log and slice into 1/4 inch rounds, rotating the log 1/4 turn after each slice to maintain shape. Put dough back into freezer between batches. Place on ungreased cookie sheet — cookies might need to be reshaped into circles at this point.
Bake 7 minutes or until edges are golden. Cool cookies on sheets 2 minutes on wire rack; remove cookies from sheets and cool completely.