Preheat the oven to 350 degrees . Using an electric mixer, cream the butter and sugar, then mix in the eggs. On low speed, mix in the flour, cocoa powder, cocoa nibs (if using), baking powder and salt. Transfer the cookie dough to a greased cookie sheet and shape into a 1-by-5-by-6-inch log. Bake for 20 minutes; let cool for 20 minutes. Leave the oven on.
On a work surface, using a serrated knife, cut the log crosswise into 12 slices. Return the slices to the baking sheet, cut side down, and bake until firm, about 15 minutes. Let the biscotti cool completely on the pan.
In a large saucepan, heat the coffee, chocolate syrup, liqueur and vodka over medium heat. Pour into mugs, top with the whipped cream and serve with the biscotti.