In the microwave or in a saucepan set over medium heat, melt the butter. Add in the espresso and cocoa powder, whisking until no lumps remain.
Spread the butter mixture evenly over the dough. Top it with the brown sugar, rubbing the sugar into the butter mixture. Top with mini chocolate chips.
Begin rolling up the dough from the shorter side. Cut the dough into 12 pieces and place the rolls evenly spaced apart in the prepared baking dish.
Cover the pan lightly with plastic wrap or a towel, and leave to rise until doubled in size, ~1 hr.
Once the dough has doubled in size, preheat the oven to 350°F / 175°C. Place the rolls in the oven and bake for 20 minutes, or until the tops of the rolls are golden brown.