30 mintues before the dough is finished rising, make the filling. Combine the butter, chocolate, sugar, cocoa powder, espresso powder, vanilla, and salt in a small saucepan, whisking until smooth.
Set the saucepan over medium-low heat and stir every so often until the chocolate is fully melted and you're left with a relatively thick mixture.
If it gets too thick while you're rolling out the dough, you can warm it up again or add a bit of milk or cream. You want it to be spreadable, not runny and not too thick.
Punch the dough down using the fist of your hand (this will help expel some gases), and turn the dough out onto a lightly floured surface. Roll the dough into a 12x18-inch rectangle.
Evenly spread the filling all over the dough using an offset spatula or a knife, leaving a 1/2-inch border on each side.
Starting on one of the long ends, tightly roll the dough from end to end and gently press the edges together to seal.
Cut the dough into 1 1/2-inch thick sections using a sharp knife or a stand of unscented dental floss. Place the rolls in 2 lightly greased muffin tins (this recipe makes about 24 buns, so you'll need 2 (12-cup) muffin tins or 1 (24-cup muffin tin).
Cover the muffin tins with plastic wrap and let them rest in a warm spot until the rolls have doubled in size, about 1 hour.
Preheat the oven to 350°F. Bake the buns until they're golden brown and puffed up, about 20 to 25 minutes (Tip: make sure your oven racks are spaced a good bit apart becuase these rise quite a bit and you don't want them hitting another oven rack).
Remove from the oven and cool completely on wire racks.