Combine all ingredients in large pot. Bring to boil over high heat, stirring until sugar dissolves. Reduce heat to medium and simmer until apples are soft and translucent and cider coats apples thickly, stirring occasionally, about 2 hours. Transfer to bowl and cool. DO AHEADCan be made 1 week ahead. Cover and chill. Bring to room temperature before serving.
Preheat oven to 350°F. Butter 9x9x2-inch metal baking pan. Whisk first 7 ingredients in medium bowl to blend. Using electric mixer, beat butter in large bowl until fluffy. Add brown sugar and egg and beat until blended. Beat in molasses, then flour mixture. Using rubber spatula, stir in 1/2 cup boiling water. Transfer batter to prepared pan.
Bake gingerbread until tester inserted into center comes out clean, about 40 minutes. Transfer pan to rack and cool gingerbread completely in pan. DO AHEADCan be made 1 day ahead. Cover pan with foil; let stand at room temperature.
Preheat oven to 325°F. Combine milk, fresh ginger, and peppercorns in heavy medium saucepan; bring to simmer. Remove from heat. Whisk eggs, sugar, vanilla, ground ginger, and salt in medium bowl to blend. Gradually whisk hot milk mixture into egg mixture. Strain custard into medium bowl; discard solids in strainer.
Cut enough gingerbread into 1/2-inch cubes to measure 5 1/3 cups (reserve any remaining gingerbread for another use). Divide gingerbread cubes among eight 3/4-cup custard cups or ramekins. Pour custard over gingerbread in each cup, dividing equally. Let stand 15 minutes to allow gingerbread to absorb some custard.
Place cups in roasting pan. Pour enough hot water into pan to come halfway up sides of cups. Cover pan with foil. Bake puddings until set, about 1 hour. Remove from water bath.
Serve puddings warm or at room temperature, topped with candied apple garnish and ice cream.