Preheat oven to 350 degrees F.
In the bowl of a stand mixer, combine sugar, hot water, eggs, instant coffee , vanilla and peppermint extracts and beat until smooth and creamy.
In a separate bowl, whisk together flour, cocoa, baking soda and salt. Add to mixer and combine on low speed until just combined.
The batter will be sticky. Line a large baking sheet or two smaller cookie sheets with silpat or parchment paper. Stir together 2 tablespoons of flour and cocoa powder and sprinkle onto the prepared baking sheets. Divide dough in half and press dough into two rectangles on the dusted baking sheet(s), about 4 inches by 10 inches, and 1/4 inch thick.
Bake for 15-20 minutes. Remove from oven and let cool 10 minutes. Slice into 3/4-inch slices and lay each slice on it’s side and put back in the oven for an additional 15 minutes.
Remove from oven and allow to cool completely on wire rack.
In a wide, shallow, microwave-safe dish, melt white chocolate according to package directions. Dip biscotti into the melted chocolate, one at a time and sprinkle with crushed candy canes, if using, and set on wax paper to set for about an hour. Store in an air-tight container for up to one week.