In a 2-quart saucepan, over high heat, heat 1 8-Oz Package dried apricots and 2 1/2 cups water to boiling. Reduce heat to low; cover and simmer 15 minutes or until apricots are tender. Drain.
In blender, blend apricots with 3/4 cup sugar and, if desired, 1/4 teaspoon 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 (see below). No need to frost, rolls are very sweet.