Prepare bread dough through its first rise.
In a 2-quart saucepan, over high heat, heat dried apricots and water to boiling. Reduce heat to low; cover and simmer 15 minutes or until apricots are tender. Drain.
In blender, blend apricots with sugar and, if desired, cinnamon. Cool.
Roll out dough as for cinnamon rolls. Spread with apricot filling. Roll as for cinnamon rolls. Cut into wedges 2 1/2 inches at wide side and 1 inch at short side.
Place wedges, short side up, on cookie sheets. Press top with finger to form butterfly-like wings. Let rise until doubled.
Beat 1 egg and brush onto rolls.
Bake at 350 degrees until golden. Baste with melted butter during baking.
No need to frost, rolls are very sweet.