Dough:
1/4 cup instant espresso powder
2 cups very hot milk, at 190 degrees F (88 degrees C)
2 1/4 teaspoons active dry yeast
1 large egg, beaten
Filling:
1/2 cup unsalted butter
3/4 cup brown sugar
1 tablespoon instant espresso powder
1 tablespoon unsweetened cocoa
Icing:
1 1/4 cups confectioner's sugar
3 tablespoons espresso or strong coffee, or more as needed
2 tablespoons white sugar
3/4 teaspoon fine salt
6 tablespoons unsalted butter, melted
4 cups all-purpose flour, or more as needed
Combine 1/4 cup instant espresso and hot milk in the bowl of a stand mixer, and let cool until just warm to the touch, about 95 degrees F (35 degrees C).
Add yeast, egg, white sugar, salt, and 6 tablespoons melted butter. Add most of the flour, attach the dough hook, and knead on low speed until everything comes together and begins to pull away from the sides of the bowl. Turn mixer speed up a notch, and continue to knead until a smooth, soft, elastic dough forms, adding in remaining flour as needed, 3 to 4 minutes.
Remove dough from the mixer, form into a ball, and place back in the bowl. Cover and let it rise in a warm place until doubled in size, 1 to 2 hours.
Meanwhile, make filling. Melt 1/2 cup butter in a small pan over medium heat. Stir in brown sugar, cocoa, and 1 tablespoon instant espresso powder. Once combined, remove from heat and let cool. As soon as butter starts to cool and solidify, stir to form a thick, spreadable paste. Reserve until needed.
Once dough has risen, use your hands to press out the air, and reshape into a ball. For best results, transfer dough to a plastic bag and place in the refrigerator overnight. Dough can be used right away if need be.
Very lightly flour a work surface. Turn dough out onto the work surface, press into a rectangle, and very lightly dust the top with flour. Roll out into a 12x18-inch rectangle.
Spread filling evenly to the edges, leaving a few inches along one of the long sides free of filling. Lightly brush exposed dough with water; this will help to seal the seam.
Beginning with the long side that has filling, roll dough and filling toward the long side with exposed dough to form a uniform log, finishing with the seam on the bottom.
Generously butter a 9x12- or 13-inch baking dish or pan, and, if desired, line the bottom with buttered parchment. Score the log of dough into 12 equal portions, and then cut each portion with a piece of string as shown.
Place cut rolls into the prepared pan. Cover rolls and leave to rise in a warm spot until doubled in size, 1 to 2 hours.
Preheat the oven to 375 degrees F (190 degrees C).
Bake in the preheated oven until puffed, golden brown at the edges, and an instant-read thermometer inserted into the center, reads 200 degrees F (95 degrees C), about 30 minutes.
Let cool for 15 minutes before icing.
Whisk together confectioner’s sugar with 3 to 4 tablespoons of espresso or strong coffee, or enough to form an icing that can be drizzled over with a spoon.
Drizzle icing over rolls and let cool before serving, or enjoy slightly warm.