Make the biscotti: Preheat the oven to 400 degrees F. Line a baking sheet with parchment paper. Whisk the flour, caraway seeds, baking soda and salt in a medium bowl; stir in the raisins. Add the buttermilk and stir with a wooden spoon until combined. Gather the dough into a ball, then transfer to the prepared baking sheet. Form into a small log, about 8 inches long and 5 inches wide. Bake until golden, about 45 minutes.
Remove from the oven and reduce the temperature to 350 degrees F. Let the log cool 30 minutes, then transfer to a cutting board and slice crosswise into 1/4-inch-thick pieces. Arrange cut-side down on an unlined baking sheet, brush with the melted butter and sprinkle with the sugar. Bake until lightly golden, about 20 minutes. Transfer to a rack; let cool.
Assemble the desserts: Fill 6 mugs halfway with coffee and add a splash of whisky to each. Add 2 scoops of ice cream to each mug and serve with the biscotti.