Roll pastry in a rectangle about ⅛" thick. Cut in 6 squares.
Peel and pit firm, ripe peaches, using care to keep peaches whole. Fill cavity in each peach with 1 tblsp. granulated sugar and 1 tblsp. butter. Place peaches in center of pastry squares and mold pastry around peaches to cover completely. Dust lightly with cinnamon. Place dumplings in a deep pan.