Add the milk, butter, and sugar to a microwave safe bowl.
Heat in 30 second increments until the butter is completely melted and the mixture is hot. Stir well to combine, then leave to cool to just above room temperature.
Add the active dry yeast to the milk mixture and allow to sit for 10 minutes, or until a foam forms on top.
While the yeast is proofing in the milk, add the flour, baking powder, and salt to a mixing bowl of a stand mixer.
Add the instant coffee to the milk mixture, then mix in the flour mixture until well combined. Use a dough hook to knead the dough on medium speed for about 10 minutes.
Lightly grease a large bowl and add the dough. Cover tightly with a plastic wrap and leave in a warm, dry place for one hour, or until doubled in size.
While the dough is rising, mix together the butter and instant coffee for the filling and heat until the butter is melted. In a separate bowl, mix together both sugars and the cinnamon for the filling together.
Lightly flour a flat surface and place the dough on your surface. Roll out until it is roughly 16 x 11 inches – this does not need to be completely accurate.
Stir the butter mixture vigorously, then spread on the dough, leaving a small border around the edges. You won’t need all the butter, reserve the remaining butter. Spread the cinnamon sugar mixture over the butter and gently press down to adhere.
Roll the dough along the long side so you have a long log in front of you. Cut the log into 8 equal pieces. Take the leftover coffee butter mixture and grease a 9 x 13 baking pan with the butter and place the cinnamon rolls cut side down in the pan. Cover with plastic wrap and allow to rise for 30 minutes.
While the dough is rising, preheat the oven to 350 F.
Bake the rolls for about 25 – 30 minutes, or until fluffy and a light golden brown.
While the rolls are baking, mix together the ingredients for the frosting. Add the heavy cream if you want a thinner frosting.