Preheat oven to 375°. Stir together first 3 ingredients; cut shortening into flour mixture with a pastry blender until crumbly. Gradually add milk, stirring just until dry ingredients are moistened.
Turn dough out onto a lightly floured surface, and knead lightly 4 to 5 times. Shape into a 12-inch log. Cut log into 6 (2-inch) pieces. Shape each into a disk, and roll each into an 8-inch circle on a lightly floured surface.
Peel pears, reserving peels. Core each pear from bottom, leaving top 2 inches and stems intact.
Stir together brown sugar and next 2 ingredients; spoon about 1 1/2 Tbsp. brown sugar mixture into each pear cavity, pressing firmly. Sprinkle remaining sugar mixture in center of pastry circles (about 1 1/2 Tbsp. each). Place 1 pear in center of each pastry circle. Dot pears with 1/4 cup softened butter. Press dough around pears with palms of hands, sealing around stem. 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, if necessary.
Bring granulated sugar, next 3 ingredients, reserved pear peels, and 1 1/2 cups water to a boil over medium-high heat, stirring constantly. Boil, stirring constantly, 1 minute or until sugar is dissolved. Reduce heat to low. Cook, stirring occasionally, 5 minutes. Pour through a wire-mesh strainer into a bowl; discard solids. Pour syrup over dumplings. Serve immediately.