In a medium bowl, mix the butter, sugar, cinnamon, instant coffee, salt, and vanilla.
Place the dough onto a lightly floured surface and roll the dough into a 10x14 rectangle (around 1/4 inch thick). Evenly spread the filling over the dough. Starting from the long end, roll the dough down to the bottom edge until you have one long roll. Using a string or sharp knife, cut the dough into 8-9 equal rolls.
In a cast iron or baking dish, spread butter and light brown sugar on the bottom of the pan. Place the buns on the prepared dish and cover it with a clean kitchen towel. Let it rest for 40-45 min at room temp.
Preheat the oven to 350F.
In a small bowl, combine 1/3 cup heavy cream and 1 tbsp instant coffee. Uncover the rolls and pour the coffee and cream mixture over them. Bake the rolls for about 25-30 minutes or until golden. Remove them from the oven and let them cool for 10 min.