Add sugar, salt, butter pieces, eggs, water, bread flour and yeast to bread machine pan in that order. Select dough cycle.
Remove dough from machine to a lightly floured surface. Knead in enough flour to make the dough easy to handle.
Divide dough into 3 portions. Divide each portion into 6 equal pieces. Divide each piece into 3 portions and roll to form a small ball. There will be a total of 54.
Place 3 balls into each section of a 2-1/2 inch muffin cup that has been greased or coated with non-stick spray; makes a total of 18 clover leaf rolls. Cover and let rise in a warm place until doubled in size, about 20 to 30 minutes.
Brush tops of rolls with lightly beaten egg and bake in preheated 375°F oven for 12 to 14 minutes, or until done.