Prepare the dough: Heat the buttermilk over medium-low heat to 105°F to no more than 110°F. In a medium bowl combine the buttermilk, espresso and 1 tablespoon of the granulated sugar. Sprinkle with the yeast and let sit for 5 minutes until foamy. Whisk the eggs and vanilla into the yeast mixture until smooth.
In the bowl of a standing mixer, combine the flour, remaining sugar (⅓ cup minus 1 tablespoon), salt, and espresso powder using the paddle attachment. With the mixer on the lowest speed, slowly add the milk mixture until combined. Add the butter 1 piece at a time beating until incorporated before adding the next pieceIncrease the speed to medium-high for 5 minutes. The dough will be silky, smooth and have pulled away from the sides of the bowl.
Transfer the dough to an oiled bowl and cover with plastic wrap or a kitchen towel. Let rise for 1 to 2 hours in a warm spot or until double in size. While the dough rises, grease a 9x13 baking dish with butter and set aside. (see notes for faster rise tips)
Once the dough has doubled in size, tip the dough out onto a well floured surface. Roll out into an 18" x 12" large rectangle.
For the filling: in a small bowl, combine the melted butter and coffee liquer and brush all over the dough. Sprinkle the granulated sugar over the dough, leaving a ½" to 1" border. Top with dollops of mascarpone cheese all over the dough.
Tightly roll the dough from one long end to the other. Using a string or a sharp serrated knife, cut the dough log into 1" rounds. Brush with 2 tablespoons melted butter, cover with a kitchen towel and let rise for 30 to 45 minutes in a warm place.
Preheat the oven to 350°F. Bake the buns for 45 to 50 minutes - cover the buns with aluminum foil for the last 15 minutes of baking if they've started to brown by the 30 minute mark.
Make the frosting: In a medium bowl, whisk together the softened mascarpone and powdered sugar. Add the Kahlua or coffee liquer and slowly increase the speed until the liquid is combined and a smooth frosting is formed.
Pour the frosting over the freshly baked buns and serve immediately. If serving at a later time, reheat the buns in the baking dish then pour the frosting over just before serving.