In a large bowl, combine the flour, active dry yeast, sugar, and salt. Add the lukewarm milk, egg, and softened butter. Knead until a smooth dough forms. Cover the bowl with a cloth and let the dough rise in a warm place for about an hour, or until doubled in size.
Combine the softened butter, brown sugar, cinnamon, cocoa powder, and instant coffee powder into a spreadable paste.
On a lightly floured surface, roll out the dough into a rectangle (about 12x20 inches).
Spread the cinnamon-coffee filling evenly over the rolled-out dough.
Roll up the dough lengthwise and then cut the roll into about 12 equal slices.
Place the cinnamon rolls on a greased or parchment-lined baking pan. Cover and let them rise for another 30 minutes.
Preheat oven to 350°F. Brush the rolls with the beaten egg. Bake for about 25 minutes, or until golden brown.
Whisk together the powdered sugar with 1-2 tablespoons of strong coffee or espresso to make a smooth glaze.
Let the cinnamon rolls cool slightly and then glaze.
