In a large mixing bowl, combine yeast, flour, sugar and salt. Melt the butter in the microwave and add the milk and water. Heat this liquid mixture in the microwave until it reaches 110 F.
Add the butter mixture to the dry ingredients in the bowl. Mix together using a wooden spoon. Add the egg, then add the remaining flour little by little, mixing after each addition. Only add sparingly-you will not need the entire 1/2 cup. You only need to see the dough gather in the center and cleaning the sides of the bowl. After this consistency is achieved, stop adding the flour.
Turn the dough over in a floured board. Knead for about ten minutes, adding a little flour just to avoid the dough from sticking to the board or to your hands. From sticky and shaggy, the dough will be smooth, elastic and can stretch thinly if you take a little portion out and spread it using your fingers.
Let the dough rest for ten minutes. Roll it into an 8 x 17 inches rectangle. Trim the edges to make the rectangle straight. Spread the melted butter over the surface. Combine sugar and cinnamon and sprinkle this mixture over the butter.
With the long side nearest you, roll the dough into a tight log. Once rolled, squeeze and stretch the log so it becomes longer and thinner. Use a sharp knife to cut the log into 1-inch portions. In between cuttings, squeeze and stretch the log from time to time to make it thinner and longer. You can make somewhere between 30-40 portions. Place the mini rolls on a buttered 24 holes mini muffin tray (or trays). If you only have one mini muffin tray, you can place the rest of the buns in any greased baking dish. Press the rolls down so that they are about the same height.
Let the dough rise: Cover the rolls with plastic wrap and let rise at room temperature for 12 hours OR pre-heat oven to 200 F. Once the oven reaches the temperature, turn off heat and place the rolls inside with the door closed. Let rise for 60 minutes. Then remove from oven.
Preheat oven to 350 F. Bake the rolls for 15-20 minutes or until lightly golden. Once slightly cool, drizzle with the coffee glaze.