Combine first 3 ingredients; cut in shortening with a pastry blender until mixture is crumbly. Gradually add milk, stirring enough to make a soft dough.
Turn dough out onto a lightly floured surface, and roll into a 21- x 14-inch rectangle. Cut rectangle into 6 (7-inch) squares with a pastry cutter.
Peel pears, reserving skin. Core each pear from the bottom, leaving top 2 inches. Place each pear on a pastry square.
Stir together brown sugar, cinnamon, and chopped nuts; spoon 2 teaspoonfuls mixture into each pear core, pressing firmly. Dot tops of pears evenly with butter. Moisten dumpling edges with water. Bring corners to center, pinching edges to seal. Place in a lightly greased 13- x 9-inch baking dish.
Bake at 375° for 40 to 50 minutes, shielding with aluminum foil after 30 minutes to prevent excessive browning.
Bring reserved pear skin, sugar, and next 4 ingredients to a boil in a medium saucepan over medium-high heat. Reduce heat, and simmer, stirring occasionally, 4 minutes or until butter melts and sugar dissolves. Remove from heat. Pour through a wire-mesh strainer into a bowl, discarding solids. Pour syrup over dumplings. Serve immediately.