In a small bowl, combine yeast with 1 teaspoon granulated sugar and warm milk. Let sit for 5 minutes or until yeast is activated and mixture is foamy.
In a large bowl, sift together bread flour, ¼ cup sugar, and salt. Add yeast mixture, egg, and butter and mix to combine. Knead until dough is smooth, about 7-8 minutes. Transfer dough to a clean bowl, cover, and let rise in a warm place until doubled in size, about 1 hour.
Punch down dough and divide into 12 pieces. Roll each piece into a ball. Place them on two lined baking sheets and loosely cover. Let rise for 1 hour.
Preheat oven to 350 degrees F.
Making the topping. Dissolve instant coffee in warm water. Whip together softened butter with sugar until well combined. Add eggs and instant coffee mix, stirring until combined. Sift 1 cake flour and add to wet ingredients, stirring just until combined. Transfer coffee topping to a piping bag. Pipe the coffee frosting on each roll, making sure the piped lines are touching each other.
Bake rolls for 15-20 minutes or until topping has set and rolls are browned. Remove from oven and cool slightly before serving.